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8.6: Rational Expressions- Answers to the Homework Exercises

Last updated

Oct 3, 2021
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- 8.5: Compound Rational Expressions
- 9: Rational Equations and Applications

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Reduce Rational Expressions

$\dfrac{1}{2}$

undefined; $a=-1$ is an excluded value

$-10$

$-8,4$

$0,-10$

$0,-\dfrac{1}{2}$

$\dfrac{3}{5a}$

$\dfrac{3m-4}{10}$

$\dfrac{1}{x+7}$

$\dfrac{n+6}{n-5}$

$\dfrac{2x-7}{5x-7}$

$\dfrac{2n-1}{9}$

$\dfrac{9x}{2}$

$\dfrac{1}{9}$

$\dfrac{7r+8}{8r}$

$\dfrac{3(x-3)}{5x+4}$

$\dfrac{9}{p+2}$

$\dfrac{2(m+2)}{5m-3}$

$\dfrac{7n-4}{4}$

$\dfrac{7a+9}{2(3a-2)}$

$\dfrac{5b-8}{5b+2}$

$\dfrac{7x-6}{(3x+4)(x+1)}$

Multiply and Divide Rational Expressions

$4x^2$

$\dfrac{3x^2}{2}$

$\dfrac{r-6}{r+10}$

$\dfrac{x-10}{7}$

$\dfrac{4(m-5)}{5m^2}$

$\dfrac{b+2}{8b}$

$\dfrac{1}{a+7}$

$9m^2(m+10)$

$\dfrac{5b}{b+5}$

$\dfrac{14}{3}$

$\dfrac{5p}{2}$

$x+4$

$\dfrac{1}{v-10}$

$\dfrac{p-10}{p-4}$

$\dfrac{v-9}{5}$

$\dfrac{7}{8(k+3)}$

$\dfrac{10}{9(n+6)}$

$n+3$

$\dfrac{3}{2}$

$\dfrac{1}{a+2b}$

$\dfrac{x-3}{5x+2}$

$\dfrac{x+1}{3x+2}$

Obtain the Lowest Common Denominator

$18$

$6a^2c^3$

$x^2-x-12$

$20xy$

$x^2-2x-3$

$12a^4b^5$

$(x+2)(x-4)$

$(x+1)(x+2)(x+3)$

$4(x-2)$

$(x-3)^2(x+3)$

$\dfrac{6a^4}{10a^3b^2},\:\dfrac{2b}{10a^3b^2}$

$\dfrac{x^2-4x}{(x-4)^2(x+4)},\:\dfrac{3x^2+12x}{(x-4)^2(x+4)}$

$\dfrac{4x}{(x-3)(x+2)},\:\dfrac{x^2+4x+4}{(x-3)(x+2)}$

$\dfrac{5}{x(x-6)},\:\dfrac{2x-12}{x(x-6)},\:\dfrac{-3x}{x(x-6)}$

$\dfrac{3x^2+4x+1}{(x-4)(x+3)(x+1)},\:\dfrac{2x^2-8x}{(x-4)(x+3)(x+1)}$

Add and Subtract Rational Expressions

$\dfrac{6}{a+3}$

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

$\dfrac{15t+16}{18t^3}$

$\dfrac{-7x-13}{4x}$

$\dfrac{-z^2+5z}{z^2-1}$

$\dfrac{4t-5}{4(t-3)}$

$\dfrac{t^2+2ty-y^2}{y^2-t^2}$

$\dfrac{x-8}{(x+8)(x+6)}$

$\dfrac{2x+4}{x^2+4x+3}$

$\dfrac{a-2}{a^2-9}$

$\dfrac{5(x-1)}{(x+1)(x+3)}$

$x-4$

$\dfrac{3x+4}{x^2}$

$\dfrac{5x+9}{24}$

$\dfrac{-c^2+cd-d^2}{c^2d^2}$

$\dfrac{11x+15}{4x(x+5)}$

$\dfrac{2x+10}{(x+3)^2}$

$\dfrac{2x^2-10x+25}{x(x-5)}$

$\dfrac{2x-5}{(x-3)(x-2)}$

$\dfrac{2x+7}{x^2+5x+6}$

$\dfrac{2}{y^2-y}$

$\dfrac{5x+5}{x^2+2x-15}$

$\dfrac{x+1}{x+2}$

$\dfrac{x-4}{x+2}$

Compound Rational Expressions

$\dfrac{x}{x-1}$

$-\dfrac{a-1}{a+1}$

$-\dfrac{1}{2}$

$\dfrac{x}{3}$

$\dfrac{x-5}{x+9}$

$\dfrac{x-2}{x+2}$

$\dfrac{5-a}{a}$

$\dfrac{4}{5}$

$\dfrac{2a^2-3a+3}{-4a^2-2a}$

$\dfrac{x+2}{x-1}$

$\dfrac{1}{x+4}$

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

$\dfrac{a-3b}{a+3b}$

$\dfrac{-2a-2}{3a-4}$

$-\dfrac{2x}{x^2+1}$

Reduce Rational Expressions

Multiply and Divide Rational Expressions

Obtain the Lowest Common Denominator

Add and Subtract Rational Expressions

Compound Rational Expressions

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