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#