8.6 Solve Rational Equations

If you miss a problem, go back to the section listed and review the material.

Solve: $\frac{1}{6} x + \frac{1}{2} = \frac{1}{3} .$
If you missed this problem, review the reference.

Solve: $n^{2} - 5 n - 36 = 0 .$
If you missed this problem, review the reference.

Solve for $y$ in terms of $x$: $5 x + 2 y = 10$ for $y .$
If you missed this problem, review the reference.

Solve: $\frac{1}{y} + \frac{2}{3} = \frac{1}{5} .$

Solve: $\frac{2}{3} + \frac{1}{5} = \frac{1}{x} .$

Solve: $1 - \frac{2}{a} = \frac{15}{a^{2}} .$

Solve: $1 - \frac{4}{b} = \frac{12}{b^{2}} .$

Solve: $\frac{1}{x - 1} = \frac{2}{3 x} .$

Solve: $\frac{3}{5 n + 1} = \frac{2}{3 n} .$

Solve: $\frac{2}{x + 1} + \frac{1}{x - 1} = \frac{1}{x^{2} - 1} .$

Solve: $\frac{5}{y + 3} + \frac{2}{y - 3} = \frac{5}{y^{2} - 9} .$

Solve: $\frac{2}{x + 5} - \frac{1}{x - 1} = 1 .$

Solve: $\frac{3}{x + 8} - \frac{2}{x - 2} = 1 .$

Solve: $\frac{x + 13}{x^{2} - 7 x + 10} = \frac{6}{x - 5} - \frac{4}{x - 2} .$

Solve: $\frac{y - 14}{y^{2} + 3 y - 4} = \frac{2}{y + 4} + \frac{7}{y - 1} .$

Solve: $\frac{x}{18} + \frac{x + 6}{9 x} = \frac{2}{3 x} .$

Solve: $\frac{y + 5}{5 y} + \frac{y}{15} = \frac{1}{y} .$

Solve: $\frac{x}{x + 4} = \frac{32}{x^{2} - 16} + 5 .$

Solve: $\frac{y}{y + 8} = \frac{128}{y^{2} - 64} + 9 .$

Solve: $\frac{y}{5 y - 10} - \frac{5}{3 y + 6} = \frac{2 y^{2} - 19 y + 54}{15 y^{2} - 60} .$

Solve: $\frac{z}{2 z + 8} - \frac{3}{4 z - 8} = \frac{3 z^{2} - 16 z - 16}{8 z^{2} + 16 z - 64} .$

Solve: $\frac{A}{L} = W$ for $L .$

Solve: $\frac{F}{A} = M$ for $A .$

Solve: $\frac{y - 2}{x + 1} = \frac{2}{3}$ for $x .$

Solve: $x = \frac{y}{1 - y}$ for $y .$

Solve: $\frac{1}{a} + \frac{1}{b} = c$ for $a .$

Solve: $\frac{2}{x} + \frac{1}{3} = \frac{1}{y}$ for $y .$

Solve.

$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$

Solve.

$\frac{5}{2} - \frac{1}{c} = \frac{3}{4}$

Solve.

$\frac{4}{5} + \frac{1}{4} = \frac{2}{v}$

Solve.

$\frac{7}{9} + \frac{1}{x} = \frac{2}{3}$

Solve.

$1 - \frac{2}{m} = \frac{8}{m^{2}}$

Solve.

$1 + \frac{9}{p} = \frac{−20}{p^{2}}$

Solve.

$\frac{1}{r + 3} = \frac{4}{2 r}$

Solve.

$\frac{5}{3 v - 2} = \frac{7}{4 v}$

Solve.

$\frac{3}{x + 4} + \frac{7}{x - 4} = \frac{8}{x^{2} - 16}$

Solve.

$\frac{8}{z - 10} + \frac{7}{z + 10} = \frac{5}{z^{2} - 100}$

Solve.

$\frac{1}{q + 4} - \frac{2}{q - 2} = 1$

Solve.

$\frac{1}{t + 7} - \frac{5}{t - 5} = 1$

Solve.

$\frac{v - 10}{v^{2} - 5 v + 4} = \frac{3}{v - 1} - \frac{6}{v - 4}$

Solve.

$\frac{x - 10}{x^{2} + 8 x + 12} = \frac{3}{x + 2} + \frac{4}{x + 6}$

Solve.

$\frac{z}{16} + \frac{z + 2}{4 z} = \frac{1}{2 z}$

Solve.

$\frac{b + 3}{3 b} + \frac{b}{24} = \frac{1}{b}$

Solve.

$\frac{d}{d + 3} = \frac{18}{d^{2} - 9} + 4$

Solve.

$\frac{n}{n + 2} = \frac{8}{n^{2} - 4} + 3$

Solve.

$\frac{q}{3 q - 9} - \frac{3}{4 q + 12}$
$= \frac{7 q^{2} + 6 q + 63}{24 q^{2} - 216}$

Solve.

$\frac{s}{2 s + 6} - \frac{2}{5 s + 5}$
$= \frac{5 s^{2} - s - 18}{10 s^{2} + 40 s + 30}$

Solve.

$\frac{C}{r} = 2 \pi \text{for} r$

Solve.

$\frac{V}{h} = l w \text{for} h$

Solve.

$\frac{v + 3}{w - 1} = \frac{1}{2} \text{for} w$

Solve.

$a = \frac{b + 3}{c - 2} \text{for} c$

Solve.

$\frac{1}{p} + \frac{2}{q} = 4 \text{for} p$

Solve.

$\frac{2}{v} + \frac{1}{5} = \frac{3}{w} \text{for} w$

Solve.

$\frac{m + 3}{n - 2} = \frac{4}{5} \text{for} n$

Solve.

$\frac{3}{x} - \frac{5}{y} = \frac{1}{4} \text{for} y$

Solve.

$r = \frac{s}{3 - t} \text{for} t$

House Painting Alain can paint a house in 4 days. Spiro would take 7 days to paint the same house. Solve the equation $\frac{1}{4} + \frac{1}{7} = \frac{1}{t}$ for t to find the number of days it would take them to paint the house if they worked together.

Why is there no solution to the equation $\frac{3}{x - 2} = \frac{5}{x - 2}$?