5.6E: Exercises

Solve Rational Equations

Solve the following

1. \(\dfrac{1}{a}+\dfrac{2}{5}=\dfrac{1}{2}\)
2. \(\dfrac{4}{5}+\dfrac{1}{4}=\dfrac{2}{v}\)
3. \(1-\dfrac{2}{m}=\dfrac{8}{m^{2}}\)
4. \(1+\dfrac{9}{p}=\dfrac{-20}{p^{2}}\)
5. \(\dfrac{5}{3 v-2}=\dfrac{7}{4 v}\)
6. \(\dfrac{3}{x+4}+\dfrac{7}{x-4}=\dfrac{8}{x^{2}-16}\)
7. \(\dfrac{8}{z-10}-\dfrac{7}{z+10}=\dfrac{5}{z^{2}-100}\)
8. \(\dfrac{-10}{q-2}-\dfrac{7}{q+4}=1\)
9. \(\dfrac{v-10}{v^{2}-5 v+4}=\dfrac{3}{v-1}-\dfrac{6}{v-4}\)
10. \(\dfrac{x-10}{x^{2}+8 x+12}=\dfrac{3}{x+2}+\dfrac{4}{x+6}\)
11. \(\dfrac{b+3}{3 b}+\dfrac{b}{24}=\dfrac{1}{b}\)
12. \(\dfrac{d}{d+3}=\dfrac{18}{d^{2}-9}+4\)
13. \(\dfrac{n}{n+2}-3=\dfrac{8}{n^{2}-4}\)
14. \(\dfrac{q}{3 q-9}-\dfrac{3}{4 q+12}=\dfrac{7 q^{2}+6 q+63}{24 q^{2}-216}\)
15. \(\dfrac{s}{2 s+6}-\dfrac{2}{5 s+5}=\dfrac{5 s^{2}-3 s-7}{10 s^{2}+40 s+30}\)
16. \(\dfrac{2}{x^{2}+2 x-8}-\dfrac{1}{x^{2}+9 x+20}=\dfrac{4}{x^{2}+3 x-10}\)
17. \(\dfrac{3}{x^{2}-5 x-6}+\dfrac{3}{x^{2}-7 x+6}=\dfrac{6}{x^{2}-1}\)

Answer

1. \(a=10\)
2. \(v=\dfrac{40}{21}\)
3. \(m=-2,\; m=4\)
4. \(p=-5, \; p=-4\)
5. \(v=14\)
6. \(x=-\dfrac{4}{5}\)
7. \(z=-145\)
8. \(q=-18, \; q=-1\)
9. no solution
10. no solution
11. \(b=-8\)
12. \(d=2\)
13. \(n=1\)
14. no solution
15. \(s=\dfrac{5}{4}\)
16. \(x=-\dfrac{4}{3}\)
17. no solution