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

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Answer 1 · 2017-01-27T15:13:53

$x=-12$

This is one that is really worth remembering:

$a^2-b^2=(a-b)(a+b)$

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

$(3(x-6)-(x+6))/(x^2-6^2) =(4x)/(x^2-6^2)$

$3(x-6)-(x+6)=4x$

$2x-24=4x$

$2x=-24$

$x=-12$

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