How do you combine #\frac { w + 8} { w - 4} + \frac { w - 4} { w + 8}#?

1 Answer
ceenik
Apr 25, 2017

#(2(w^2+4w+40))/((w-4)(w+8))#

Explanation:

#\frac { w + 8} { w - 4} + \frac { w - 4} { w + 8}#

First, give both fractions common denominators by multiplying their denominators with each other [Whatever we do to the denominator we must also do to the numerator]

#(\frac { w + 8} { w - 4})((w+8)/{w+8))# + #(\frac { w - 4} { w + 8})((w-4)/{w-4))#

#((w+8)^2)/((w-4)(w+8))#+#(w-4)^2/((w-4)(w+8))#

#((w^2+16w+64))/((w-4)(w+8))#+#((w^2-8w+16))/((w-4)(w+8))#

#(w^2+16w+64+w^2-8w+16)/((w-4)(w+8))#

Add and subtract common terms

#(2w^2+8w+80)/((w-4)(w+8))#

Factor 2 out of the numerator

#(2(w^2+4w+40))/((w-4)(w+8))#

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