How do you evaluate #frac { a - b } { 4a + 4b } +\div \frac { a ^ { 2} - b ^ { 2} } { a ^ { 2} + 8a + 16}#?

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Answer 1 · 2017-12-03T22:50:23

#(a^2+8a+16)/(4a^2+8ab+4b^2)#

Definitely going to want to start by factoring this.

#(a-b)/(4(a+b))divide((a-b)(a+b))/(a+4)^2#

"Keep-change-flip" so we have multiplication:

#(a-b)/(4(a+b))times(a+4)^2/((a-b)(a+b))#

#color(red)cancel(color(black)(a-b))/(4(a+b))times(a+4)^2/(color(red)cancel(color(black)(a-b))(a+b))#

#(a+4)^2/(4(a+b)^2)#

If you wish, multiply out:

#(a^2+8a+16)/(4a^2+8ab+4b^2)#