How do you solve #\frac { 5} { x - 4} - \frac { 6} { x + 4} = \frac { 7} { x ^ { 2} - 16}#?

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Answer 1 · 2017-02-20T07:29:30

#x=37#

Given:

#5/(x-4)-6/(x+4) = 7/(x^2-16)#

Multiply both sides by #x^2-16 = (x-4)(x+4)# to get:

#5(x+4)-6(x-4) = 7#

Multiply out to get:

#5x+20-6x+24 = 7#

Combine like terms to get:

#-x+44 = 7#

Add #x-7# to both sides to get:

#37=x#

This is an authentic solution of the original equation, since it results in non-zero denominators.