5.6E: Exercises
- Page ID
- 104864
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Solve Rational Equations
In the following exercises, solve each rational equation.
Solve the following
- \(\dfrac{1}{a}+\dfrac{2}{5}=\dfrac{1}{2}\)
- \(\dfrac{4}{5}+\dfrac{1}{4}=\dfrac{2}{v}\)
- \(1-\dfrac{2}{m}=\dfrac{8}{m^{2}}\)
- \(1+\dfrac{9}{p}=\dfrac{-20}{p^{2}}\)
- \(\dfrac{5}{3 v-2}=\dfrac{7}{4 v}\)
- \(\dfrac{3}{x+4}+\dfrac{7}{x-4}=\dfrac{8}{x^{2}-16}\)
- \(\dfrac{8}{z-10}-\dfrac{7}{z+10}=\dfrac{5}{z^{2}-100}\)
- \(\dfrac{-10}{q-2}-\dfrac{7}{q+4}=1\)
- \(\dfrac{v-10}{v^{2}-5 v+4}=\dfrac{3}{v-1}-\dfrac{6}{v-4}\)
- \(\dfrac{x-10}{x^{2}+8 x+12}=\dfrac{3}{x+2}+\dfrac{4}{x+6}\)
- \(\dfrac{b+3}{3 b}+\dfrac{b}{24}=\dfrac{1}{b}\)
- \(\dfrac{d}{d+3}=\dfrac{18}{d^{2}-9}+4\)
- \(\dfrac{n}{n+2}-3=\dfrac{8}{n^{2}-4}\)
- \(\dfrac{q}{3 q-9}-\dfrac{3}{4 q+12}=\dfrac{7 q^{2}+6 q+63}{24 q^{2}-216}\)
- \(\dfrac{s}{2 s+6}-\dfrac{2}{5 s+5}=\dfrac{5 s^{2}-3 s-7}{10 s^{2}+40 s+30}\)
- \(\dfrac{2}{x^{2}+2 x-8}-\dfrac{1}{x^{2}+9 x+20}=\dfrac{4}{x^{2}+3 x-10}\)
- \(\dfrac{3}{x^{2}-5 x-6}+\dfrac{3}{x^{2}-7 x+6}=\dfrac{6}{x^{2}-1}\)
- Answer
-
- \(a=10\)
- \(v=\dfrac{40}{21}\)
- \(m=-2,\; m=4\)
- \(p=-5, \; p=-4\)
- \(v=14\)
- \(x=-\dfrac{4}{5}\)
- \(z=-145\)
- \(q=-18, \; q=-1\)
- no solution
- no solution
- \(b=-8\)
- \(d=2\)
- \(n=1\)
- no solution
- \(s=\dfrac{5}{4}\)
- \(x=-\dfrac{4}{3}\)
- no solution
Writing Exercises
- Your class mate is having trouble in this section. Write down the steps you would use to explain how to solve a rational equation.
- Alek thinks the equation \(\dfrac{y}{y+6}=\dfrac{72}{y^{2}-36}+4\) has two solutions, \(y=-6\) and \(y=4\). Explain why Alek is wrong.
- Answer
-
Answers will vary.