# How do you solve x/(x-2)-1/(x-3)=(1)?

Sep 11, 2017

color(magenta)(x=4

#### Explanation:

$\frac{x}{x - 2} - \frac{1}{x - 3} = \left(1\right)$

multiply both sides by $x - 2$

$\therefore x - \frac{x - 2}{x - 3} = x - 2$

multiply both sides by $x - 3$

$\therefore x \left(x - 3\right) - \left(x - 2\right) = \left(x - 2\right) \left(x - 3\right)$

$\therefore {x}^{2} - 3 x - x + 2 = {x}^{2} - 5 x + 6$

$\therefore {x}^{2} - {x}^{2} - 4 x + 5 x = 6 - 2$

:.color(magenta)(x=4

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substitute color(magenta)(x=4

$\therefore \frac{4}{\left(\textcolor{m a \ge n t a}{4}\right) - 2} - \frac{1}{\left(\textcolor{m a \ge n t a}{4}\right) - 3} = \left(1\right)$

$\therefore \frac{4}{2} - \frac{1}{1} = 1$

$\therefore 2 - 1 = 1$

:.color(magenta)(1=1