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

Aug 29, 2016

$x = + 3 , \mathmr{and} + 6$

#### Explanation:

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

i.e. $6 \left(x - 3\right) = x \left(x - 3\right)$

$6 x - 18 = {x}^{2} - 3 x$

${x}^{2} - 9 x + 18 = 0$

This is a quadratic in $x$, for which we might use the quadratic formula. Alternatively we could factor it to give:

$\left(x - 3\right) \left(x - 6\right) = 0$

Thus $x$ has roots at $+ 3$ or $+ 6$