# How do you solve -\frac{9}{x - 3} = - \frac{3}{x - 5}?

Sep 26, 2016

Distribute the negative and cross multiply

#### Explanation:

Distribute the negative to the numerator and cross multiply
$- 9 \left(x - 5\right) = - 9 x + 45$

$- 3 \left(x - 3\right) = - 3 x + 9$

Combine like terms by subtracting 45 on both sides of the equation
$- 9 x + 45 = - 3 x + 9$

$- 9 x = - 3 x - 36$

Combine like terms by adding 3x on both sides of the equations
$- 6 x = - 36$

Isolate x by dividing by -6
$x = 6$

Sep 26, 2016

$x = 6$

#### Explanation:

Decide what to do with the negative at the front of each fraction.
It may only be used with the numerator OR the denominator - not both.

$\frac{9}{\textcolor{red}{-} \left(x - 3\right)} = \frac{\textcolor{red}{- 3}}{x - 5} \text{ } \leftarrow$ now cross multiply

$9 \left(x - 5\right) = \textcolor{red}{+ 3} \left(x - 3\right) \text{ } \leftarrow$ remove the brackets

$9 x - 45 = 3 x - 9 \text{ } \leftarrow$ re-arrange the terms

$9 x - 3 x = 45 - 9 \text{ } \leftarrow$ simplify each side

$6 x = 36 \text{ } \leftarrow \div 6$

$x = 6$

Of course, the simplest solution with the negative signs, is to multiply each fraction by $- 1$, or move each to the other side to make each term positive.

$\frac{3}{x - 5} = \frac{9}{x - 3} \text{ } \leftarrow$ cross multiply and proceed as above.