Question

Rectangle A has an area of 4 − x^2. Rectangle B has an area of x^2 + 2x − 8. In simplest form, what is the ratio of the area of Rectangle A to the area of Rectangle B? Show your work.

Answer 1

Or, 4 - x^2 over x^2 + 2x - 8.

Answer 2

Rectangle A : 4-x^2=(2+x)(2-x)
Rectangle B : x^2 + 2x - 8 = (x+4)(x-2)
hence,
A:B = (2+x)(2-x) : (x+4)(x-2)
= -(2+x)(x-2) : (x+4)(x-2)
= -(x+2) : (x+4)