Question

PLEASE HELP A.S.A.P!
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?
Please show your work so that I can understand:)

Answer 1

The numerator and the denominator both can be factorised:
\[\frac{(2+x)(2-x)}{(x+4)(x-2)}\]
Multiply numerator and denominator by -1 to enable cancellation:
\[\frac{(2+x)(x-2)}{(x+4)(x-2)}\]
Answer is:
\[-\frac{2+x}{4+x}\]

Answer 2

Thank you so much for your help!!!

Answer 3

You're welcome :)

Answer 4

Could you explain to me real quick how you changed it from:
2+x)(2−x) over (x+4)(x−2)
to
(2+x)(x−2) over (x+4)(x−2)??
I'm kinda confused:/

Answer 5

Never mind I mean the factoring part! I dont understand facotring very well

Answer 6

The numerator of the original expression is the difference of two squares.To facorise you take the square root of each term and arrange as follows:
4 - x^2 = (2 + x)(2 - x)
To factorise the denominator you need to find factors of 8 that have a difference of 2. These are 4 and 2.
x^2 + 2x - 8 = (x + 4)(x - 2)