How do you evaluate frac { a - b } { 4a + 4b } +\div \frac { a ^ { 2} - b ^ { 2} } { a ^ { 2} + 8a + 16}ab4a+4b+÷a2b2a2+8a+16?

1 Answer
Dec 3, 2017

(a^2+8a+16)/(4a^2+8ab+4b^2)a2+8a+164a2+8ab+4b2

Explanation:

Definitely going to want to start by factoring this.

(a-b)/(4(a+b))divide((a-b)(a+b))/(a+4)^2ab4(a+b)÷(ab)(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))ab4(a+b)×(a+4)2(ab)(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)