14.2.1: Chapter 1

Last updated
Save as PDF

Page ID: 118255

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$ \newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$

( \newcommand{\kernel}{\mathrm{null}\,}\) $ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\id}{\mathrm{id}}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\kernel}{\mathrm{null}\,}$

$ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$

$ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$

$ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\AA}{\unicode[.8,0]{x212B}}$

$ \newcommand{\vectorA}[1]{\vec{#1}} % arrow$

$ \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$

$ \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vectorC}[1]{\textbf{#1}} $

$ \newcommand{\vectorD}[1]{\overrightarrow{#1}} $

$ \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} $

$ \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} $

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$\newcommand{\avec}{\mathbf a}$ $\newcommand{\bvec}{\mathbf b}$ $\newcommand{\cvec}{\mathbf c}$ $\newcommand{\dvec}{\mathbf d}$ $\newcommand{\dtil}{\widetilde{\mathbf d}}$ $\newcommand{\evec}{\mathbf e}$ $\newcommand{\fvec}{\mathbf f}$ $\newcommand{\nvec}{\mathbf n}$ $\newcommand{\pvec}{\mathbf p}$ $\newcommand{\qvec}{\mathbf q}$ $\newcommand{\svec}{\mathbf s}$ $\newcommand{\tvec}{\mathbf t}$ $\newcommand{\uvec}{\mathbf u}$ $\newcommand{\vvec}{\mathbf v}$ $\newcommand{\wvec}{\mathbf w}$ $\newcommand{\xvec}{\mathbf x}$ $\newcommand{\yvec}{\mathbf y}$ $\newcommand{\zvec}{\mathbf z}$ $\newcommand{\rvec}{\mathbf r}$ $\newcommand{\mvec}{\mathbf m}$ $\newcommand{\zerovec}{\mathbf 0}$ $\newcommand{\onevec}{\mathbf 1}$ $\newcommand{\real}{\mathbb R}$ $\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$ $\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$ $\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$ $\newcommand{\laspan}[1]{\text{Span}\{#1\}}$ $\newcommand{\bcal}{\cal B}$ $\newcommand{\ccal}{\cal C}$ $\newcommand{\scal}{\cal S}$ $\newcommand{\wcal}{\cal W}$ $\newcommand{\ecal}{\cal E}$ $\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$ $\newcommand{\gray}[1]{\color{gray}{#1}}$ $\newcommand{\lgray}[1]{\color{lightgray}{#1}}$ $\newcommand{\rank}{\operatorname{rank}}$ $\newcommand{\row}{\text{Row}}$ $\newcommand{\col}{\text{Col}}$ $\renewcommand{\row}{\text{Row}}$ $\newcommand{\nul}{\text{Nul}}$ $\newcommand{\var}{\text{Var}}$ $\newcommand{\corr}{\text{corr}}$ $\newcommand{\len}[1]{\left|#1\right|}$ $\newcommand{\bbar}{\overline{\bvec}}$ $\newcommand{\bhat}{\widehat{\bvec}}$ $\newcommand{\bperp}{\bvec^\perp}$ $\newcommand{\xhat}{\widehat{\xvec}}$ $\newcommand{\vhat}{\widehat{\vvec}}$ $\newcommand{\uhat}{\widehat{\uvec}}$ $\newcommand{\what}{\widehat{\wvec}}$ $\newcommand{\Sighat}{\widehat{\Sigma}}$ $\newcommand{\lt}{<}$ $\newcommand{\gt}{>}$ $\newcommand{\amp}{&}$ $\definecolor{fillinmathshade}{gray}{0.9}$

Try It

1.1 Real Numbers: Algebra Essentials

ⓐ $\frac{11}{1}$
ⓑ $\frac{3}{1}$
ⓒ $- \frac{4}{1}$

ⓐ4 (or 4.0), terminating;
ⓑ $0. \bar{615384},$ repeating;
ⓒ–0.85, terminating

ⓐrational and repeating;
ⓑrational and terminating;
ⓒirrational;
ⓓrational and terminating;
ⓔirrational

ⓐpositive, irrational; right
ⓑnegative, rational; left
ⓒpositive, rational; right
ⓓnegative, irrational; left
ⓔpositive, rational; right

	N	W	I	Q	Q'
a. $- \frac{35}{7}$			X	X
b. 0		X	X	X
c. $\sqrt{169}$	X	X	X	X
d. $\sqrt{24}$					X
e. 4.763763763...				X

ⓐ10
ⓑ2
ⓒ4.5
ⓓ25
ⓔ26

ⓐ11, commutative property of multiplication, associative property of multiplication, inverse property of multiplication, identity property of multiplication;
ⓑ33, distributive property;
ⓒ26, distributive property;
ⓓ $\frac{4}{9},$ commutative property of addition, associative property of addition, inverse property of addition, identity property of addition;
ⓔ0, distributive property, inverse property of addition, identity property of addition


	Constants	Variables
a. $2 π r (r + h)$	$2, π$	$r, h$
b. 2(L + W)	2	L, W
c. $4 y^{3} + y$	4	$y$

ⓐ5;
ⓑ11;
ⓒ9;
ⓓ26

10.

ⓐ4;
ⓑ11;
ⓒ $\frac{121}{3} π$ ;
ⓓ1728;
ⓔ3

11.

1,152 cm²

12.

ⓐ $−2 y −2 z or −2 (y + z);$
ⓑ $\frac{2}{t} −1;$
ⓒ $3 p q −4 p + q;$
ⓓ $7 r −2 s + 6$

13.

$A = P (1 + r t)$

1.2 Exponents and Scientific Notation

ⓐ $k^{15}$
ⓑ ${(\frac{2}{y})}^{5}$
ⓒ $t^{14}$

ⓐ $s^{7}$
ⓑ ${(−3)}^{5}$
ⓒ ${(e f^{2})}^{2}$

ⓐ ${(3 y)}^{24}$
ⓑ $t^{35}$
ⓒ ${(- g)}^{16}$

ⓐ $1$
ⓑ $\frac{1}{2}$
ⓒ $1$
ⓓ $1$

ⓐ $\frac{1}{{(−3 t)}^{6}}$
ⓑ $\frac{1}{f^{3}}$
ⓒ $\frac{2}{5 k^{3}}$

ⓐ $t^{−5} = \frac{1}{t^{5}}$
ⓑ $\frac{1}{25}$

ⓐ $g^{10} h^{15}$
ⓑ $125 t^{3}$
ⓒ $−27 y^{15}$
ⓓ $\frac{1}{a^{18} b^{21}}$
ⓔ $\frac{r^{12}}{s^{8}}$

ⓐ $\frac{b^{15}}{c^{3}}$
ⓑ $\frac{625}{u^{32}}$
ⓒ $\frac{−1}{w^{105}}$
ⓓ $\frac{q^{24}}{p^{32}}$
ⓔ $\frac{1}{c^{20} d^{12}}$

ⓐ $\frac{v^{6}}{8 u^{3}}$
ⓑ $\frac{1}{x^{3}}$
ⓒ $\frac{e^{4}}{f^{4}}$
ⓓ $\frac{27 r}{s}$
ⓔ $1$
ⓕ $\frac{16 h^{10}}{49}$

10.

ⓐ $$ 1.52 \times 10^{5}$
ⓑ $7.158 \times 10^{9}$
ⓒ $$ 8.55 \times 10^{13}$
ⓓ $3.34 \times 10^{−9}$
ⓔ $7.15 \times 10^{−8}$

11.

ⓐ $703, 000$
ⓑ $−816, 000, 000, 000$
ⓒ $−0.000 000 000 000 39$
ⓓ $0.000008$

12.

ⓐ $- 8.475 \times 10^{6}$
ⓑ $8 \times 10^{- 8}$
ⓒ $2.976 \times 10^{13}$
ⓓ $- 4.3 \times 10^{6}$
ⓔ $\approx 1.24 \times 10^{15}$

13.

Number of cells: $3 \times 10^{13};$ length of a cell: $8 \times 10^{−6}$ m; total length: $2.4 \times 10^{8}$ m or $240, 000, 000$ m.

1.3 Radicals and Rational Exponents

ⓐ $15$
ⓑ $3$
ⓒ $4$
ⓓ $17$

$5 | x | | y | \sqrt{2 y z} .$ Notice the absolute value signs around x and y? That’s because their value must be positive!

$10 | x |$

$\frac{x \sqrt{2}}{3 y^{2}} .$ We do not need the absolute value signs for $y^{2}$ because that term will always be nonnegative.

$b^{4} \sqrt{3 a b}$

$13 \sqrt{5}$

$0$

$6 \sqrt{6}$

$14 −7 \sqrt{3}$

10.

ⓐ $−6$
ⓑ $6$
ⓒ $88 \sqrt[3]{9}$

11.

${(\sqrt{9})}^{5} = 3^{5} = 243$

12.

$x {(5 y)}^{\frac{9}{2}}$

13.

$28 x^{\frac{23}{15}}$

1.4 Polynomials

The degree is 6, the leading term is $- x^{6},$ and the leading coefficient is $−1.$

$2 x^{3} + 7 x^{2} −4 x −3$

$−11 x^{3} - x^{2} + 7 x −9$

$3 x^{4} −10 x^{3} −8 x^{2} + 21 x + 14$

$3 x^{2} + 16 x −35$

$16 x^{2} −8 x + 1$

$4 x^{2} −49$

$6 x^{2} + 21 x y −29 x −7 y + 9$

1.5 Factoring Polynomials

$(b^{2} - a) (x + 6)$

$(x −6) (x −1)$

ⓐ $(2 x + 3) (x + 3)$
ⓑ $(3 x −1) (2 x + 1)$

${(7 x −1)}^{2}$

$(9 y + 10) (9 y - 10)$

$(6 a + b) (36 a^{2} −6 a b + b^{2})$

$(10 x - 1) (100 x^{2} + 10 x + 1)$

${(5 a −1)}^{- \frac{1}{4}} (17 a −2)$

1.6 Rational Expressions

$\frac{1}{x + 6}$

$\frac{(x + 5) (x + 6)}{(x + 2) (x + 4)}$

$1$

$\frac{2 (x −7)}{(x + 5) (x −3)}$

$\frac{x^{2} - y^{2}}{x y^{2}}$

1.1 Section Exercises

irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.

The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.

$−6$

$−2$

$−9$

11.

13.

-2

15.

17.

19.

21.

23.

$−6$

25.

27.

29.

$14$

31.

$−66$

33.

$–12$

35.

$–44$

37.

$–2$

39.

$−14 y - 11$

41.

$−4 b + 1$

43.

$43 z - 3$

45.

$9 y + 45$

47.

$−6 b + 6$

49.

$\frac{16 x}{3}$

51.

$9 x$

53.

$\frac{1}{2} (40 - 10) + 5$

55.

irrational number

57.

$g + 400 - 2 (600) = 1200$

59.

inverse property of addition

61.

68.4

63.

true

65.

irrational

67.

rational

1.2 Section Exercises

No, the two expressions are not the same. An exponent tells how many times you multiply the base. So $2^{3}$ is the same as $2 \times 2 \times 2,$ which is 8. $3^{2}$ is the same as $3 \times 3,$ which is 9.

It is a method of writing very small and very large numbers.

243

$\frac{1}{16}$

11.

$\frac{1}{11}$

13.

15.

$4^{9}$

17.

$12^{40}$

19.

$\frac{1}{7^{9}}$

21.

$3.14 \times 10^{- 5}$

23.

16,000,000,000

25.

$a^{4}$

27.

$b^{6} c^{8}$

29.

$a b^{2} d^{3}$

31.

$m^{4}$

33.

$\frac{q^{5}}{p^{6}}$

35.

$\frac{y^{21}}{x^{14}}$

37.

$25$

39.

$72 a^{2}$

41.

$\frac{c^{3}}{b^{9}}$

43.

$\frac{y}{81 z^{6}}$

45.

0.00135 m

47.

$1.0995 \times 10^{12}$

49.

0.00000000003397 in.

51.

12,230,590,464 $m^{66}$

53.

$\frac{a^{14}}{1296}$

55.

$\frac{n}{a^{9} c}$

57.

$\frac{1}{a^{6} b^{6} c^{6}}$

59.

0.000000000000000000000000000000000662606957

1.3 Section Exercises

When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.

The principal square root is the nonnegative root of the number.

11.

$7 \sqrt{2}$

13.

$\frac{9 \sqrt{5}}{5}$

15.

17.

$\sqrt{2}$

19.

$2 \sqrt{6}$

21.

$5 \sqrt{6}$

23.

$6 \sqrt{35}$

25.

$\frac{2}{15}$

27.

$\frac{6 \sqrt{10}}{19}$

29.

$- \frac{1 + \sqrt{17}}{2}$

31.

$7 \sqrt[3]{2}$

33.

$15 \sqrt{5}$

35.

$20 x^{2}$

37.

$7 \sqrt{p}$

39.

$17 m^{2} \sqrt{m}$

41.

$2 b \sqrt{a}$

43.

$\frac{15 x}{7}$

45.

$5 y^{4} \sqrt{2}$

47.

$\frac{4 \sqrt{7 d}}{7 d}$

49.

$\frac{2 \sqrt{2} + 2 \sqrt{6 x}}{1 −3 x}$

51.

$- w \sqrt{2 w}$

53.

$\frac{3 \sqrt{x} - \sqrt{3 x}}{2}$

55.

$5 n^{5} \sqrt{5}$

57.

$\frac{9 \sqrt{m}}{19 m}$

59.

$\frac{2}{3 d}$

61.

$\frac{3 \sqrt[4]{2 x^{2}}}{2}$

63.

$6 z \sqrt[3]{2}$

65.

500 feet

67.

$\frac{−5 \sqrt{2} −6}{7}$

69.

$\frac{\sqrt{m n c}}{a^{9} c m n}$

71.

$\frac{2 \sqrt{2} x + \sqrt{2}}{4}$

73.

$\frac{\sqrt{3}}{3}$

1.4 Section Exercises

The statement is true. In standard form, the polynomial with the highest value exponent is placed first and is the leading term. The degree of a polynomial is the value of the highest exponent, which in standard form is also the exponent of the leading term.

Use the distributive property, multiply, combine like terms, and simplify.

11.

$4 x^{2} + 3 x + 19$

13.

$3 w^{2} + 30 w + 21$

15.

$11 b^{4} −9 b^{3} + 12 b^{2} −7 b + 8$

17.

$24 x^{2} −4 x −8$

19.

$24 b^{4} −48 b^{2} + 24$

21.

$99 v^{2} −202 v + 99$

23.

$8 n^{3} −4 n^{2} + 72 n −36$

25.

$9 y^{2} −42 y + 49$

27.

$16 p^{2} + 72 p + 81$

29.

$9 y^{2} −36 y + 36$

31.

$16 c^{2} −1$

33.

$225 n^{2} −36$

35.

$−16 m^{2} + 16$

37.

$121 q^{2} −100$

39.

$16 t^{4} + 4 t^{3} −32 t^{2} - t + 7$

41.

$y^{3} −6 y^{2} - y + 18$

43.

$3 p^{3} - p^{2} −12 p + 10$

45.

$a^{2} - b^{2}$

47.

$16 t^{2} −40 t u + 25 u^{2}$

49.

$4 t^{2} + x^{2} + 4 t −5 t x - x$

51.

$24 r^{2} + 22 r d −7 d^{2}$

53.

$32 x^{2} −4 x −3$ m²

55.

$32 t^{3} - 100 t^{2} + 40 t + 38$

57.

$a^{4} + 4 a^{3} c −16 a c^{3} −16 c^{4}$

1.5 Section Exercises

The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, $4 x^{2}$ and $−9 y^{2}$ don’t have a common factor, but the whole polynomial is still factorable: $4 x^{2} −9 y^{2} = (2 x + 3 y) (2 x −3 y) .$

Divide the $x$ term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.

$7 m$

$10 m^{3}$

$y$

11.

$(2 a −3) (a + 6)$

13.

$(3 n −11) (2 n + 1)$

15.

$(p + 1) (2 p −7)$

17.

$(5 h + 3) (2 h −3)$

19.

$(9 d −1) (d −8)$

21.

$(12 t + 13) (t −1)$

23.

$(4 x + 10) (4 x - 10)$

25.

$(11 p + 13) (11 p - 13)$

27.

$(19 d + 9) (19 d - 9)$

29.

$(12 b + 5 c) (12 b - 5 c)$

31.

${(7 n + 12)}^{2}$

33.

${(15 y + 4)}^{2}$

35.

${(5 p - 12)}^{2}$

37.

$(x + 6) (x^{2} - 6 x + 36)$

39.

$(5 a + 7) (25 a^{2} - 35 a + 49)$

41.

$(4 x - 5) (16 x^{2} + 20 x + 25)$

43.

$(5 r + 12 s) (25 r^{2} - 60 r s + 144 s^{2})$

45.

${(2 c + 3)}^{- \frac{1}{4}} (−7 c - 15)$

47.

${(x + 2)}^{- \frac{2}{5}} (19 x + 10)$

49.

${(2 z - 9)}^{- \frac{3}{2}} (27 z - 99)$

51.

$(14 x −3) (7 x + 9)$

53.

$(3 x + 5) (3 x −5)$

55.

${(2 x + 5)}^{2} {(2 x - 5)}^{2}$

57.

$(4 z^{2} + 49 a^{2}) (2 z + 7 a) (2 z - 7 a)$

59.

$\frac{1}{(4 x + 9) (4 x −9) (2 x + 3)}$

1.6 Section Exercises

You can factor the numerator and denominator to see if any of the terms can cancel one another out.

True. Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms.

$\frac{y + 5}{y + 6}$

$3 b + 3$

$\frac{x + 4}{2 x + 2}$

11.

$\frac{a + 3}{a - 3}$

13.

$\frac{3 n - 8}{7 n - 3}$

15.

$\frac{c - 6}{c + 6}$

17.

$1$

19.

$\frac{d^{2} - 25}{25 d^{2} - 1}$

21.

$\frac{t + 5}{t + 3}$

23.

$\frac{6 x - 5}{6 x + 5}$

25.

$\frac{p + 6}{4 p + 3}$

27.

$\frac{2 d + 9}{d + 11}$

29.

$\frac{12 b + 5}{3 b −1}$

31.

$\frac{4 y −1}{y + 4}$

33.

$\frac{10 x + 4 y}{x y}$

35.

$\frac{9 a - 7}{a^{2} - 2 a - 3}$

37.

$\frac{2 y^{2} - y + 9}{y^{2} - y - 2}$

39.

$\frac{5 z^{2} + z + 5}{z^{2} - z - 2}$

41.

$\frac{x + 2 x y + y}{x + x y + y + 1}$

43.

$\frac{2 b + 7 a}{a b^{2}}$

45.

$\frac{18 + a b}{4 b}$

47.

$a - b$

49.

$\frac{3 c^{2} + 3 c - 2}{2 c^{2} + 5 c + 2}$

51.

$\frac{15 x + 7}{x −1}$

53.

$\frac{x + 9}{x −9}$

55.

$\frac{1}{y + 2}$

57.

$4$

Review Exercises

$−5$

$y = 24$

$32 m$

whole

11.

irrational

13.

$16$

15.

$3 a^{6}$

17.

$\frac{x^{3}}{32 y^{3}}$

19.

$a$

21.

$1.634 \times 10^{7}$

23.

25.

$5 \sqrt{3}$

27.

$\frac{4 \sqrt{2}}{5}$

29.

$\frac{7 \sqrt{2}}{50}$

31.

$10 \sqrt{3}$

33.

$−3$

35.

$3 x^{3} + 4 x^{2} + 6$

37.

$5 x^{2} - x + 3$

39.

$k^{2} - 3 k - 18$

41.

$x^{3} + x^{2} + x + 1$

43.

$3 a^{2} + 5 a b - 2 b^{2}$

45.

$9 p$

47.

$4 a^{2}$

49.

$(4 a - 3) (2 a + 9)$

51.

${(x + 5)}^{2}$

53.

${(2 h - 3 k)}^{2}$

55.

$(p + 6) (p^{2} - 6 p + 36)$

57.

$(4 q - 3 p) (16 q^{2} + 12 p q + 9 p^{2})$

59.

${(p + 3)}^{\frac{1}{3}} (−5 p - 24)$

61.

$\frac{x + 3}{x - 4}$

63.

$\frac{1}{2}$

65.

$\frac{m + 2}{m - 3}$

67.

$\frac{6 x + 10 y}{x y}$

69.

$\frac{1}{6}$

Practice Test

rational

$x = –2$

3,141,500

$16$

11.

$2 x$

13.

15.

$\frac{3 \sqrt{x}}{4}$

17.

$21 \sqrt{6}$

19.

$13 q^{3} - 4 q^{2} - 5 q$

21.

$n^{3} - 6 n^{2} + 12 n - 8$

23.

$(4 x + 9) (4 x - 9)$

25.

$(3 c - 11) (9 c^{2} + 33 c + 121)$

27.

$\frac{4 z - 3}{2 z - 1}$

29.

$\frac{3 a + 2 b}{3 b}$

Search

Text Color

Text Size

Margin Size

Font Type