### Home > PC > Chapter 6 > Lesson 6.1.1 > Problem6-18

6-18.

Solve each equation for $x$.

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

Multiply each term by $x\left(x − 1\right)$.
Simplify.
Solve.

$\frac{x(x-1)(x)}{x-1}-\frac{x(x-1)}{x(x-1)}=3x(x-1)$

$x^{2} − 1 = 3x^{2} − 3x$
$2x^{2} − 3x + 1 = 0$
$\left(2x − 1\right)\left(x − 1\right) = 0$

$x=\frac{1}{2}\text{ or }x\neq 1 \text{ undefined}$

1. $\frac { x } { x ^ { 2 } - 25 } + \frac { 1 } { x + 5 } = 1$

Use a similar process as part (a).
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