# How do you solve  (x - 3) /x = (x - 3) / (x - 6) ?

Feb 18, 2017

$x = 3$

#### Explanation:

Put the equation in $y = 0$ form:

$y = \frac{x - 3}{x} = \frac{x - 3}{x - 6}$

$y = \frac{x - 3}{x} - \frac{x - 3}{x - 6} = 0$

Find a common denominator:
$y = \frac{x - 3}{x} \cdot \frac{x - 6}{x - 6} - \frac{x - 3}{x - 6} \cdot \frac{x}{x} = 0$

Combine under the same denominator:

$y = \frac{\left(x - 3\right) \left(x - 6\right) - x \left(x - 3\right)}{x \left(x - 6\right)} = 0$

Factor the numerator: $\left(x - 3\right) \left(x - 6 - x\right) = - 6 \left(x - 3\right)$

$y = \frac{- 6 \left(x - 3\right)}{x \left(x - 6\right)} = 0$

The numerator gives a a solution when $y = 0$, when $x = 3$