# How do you solve \frac { 3} { x + 6} - \frac { 1} { x - 6} = \frac { 4x } { x ^ { 2} - 36}?

Jan 27, 2017

$x = - 12$

#### Explanation:

This is one that is really worth remembering:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

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Spot that we can manipulate the denominators to give us 'the difference of 2 squares'.

$\frac{3 \left(x - 6\right) - \left(x + 6\right)}{{x}^{2} - {6}^{2}} = \frac{4 x}{{x}^{2} - {6}^{2}}$

$3 \left(x - 6\right) - \left(x + 6\right) = 4 x$

$2 x - 24 = 4 x$

$2 x = - 24$

$x = - 12$