how would you simplify this

Question

((x^2+2xy+y^2-16)/(16x^4-16y^4))/((x+y-4)/(4x^2+4y^2))*((x+y)/(x+y+4))

Answer 1

two things to remember:
- to divide by a fraction, keep the first fraction the way it is, and multiply by the reciprocal of the second.
- there is a lot of factoring here,
such as
(x^2 + 2xy + y^2 - 16
= (x+y)^2 - 16
= (x+y+4)(x+y-4)

and
16x^4 - 16y^4
= 16(x^2+y^2)(x+y)(x-y)

so in factored form and the reciprocal formed your question is

[(x+y+4)(x+y-4)]/[16(x^2+y^2)(x+y)(x-y)] * 4(x^2+y^2)/(x+y-4) * (x+y)/(x+y+4)
= 1/[4(x-y)]

(hope I didn't make a typo)

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