Question

What is the common denominator of (5/x^2-4) - (2/x+2) in the complex fraction (2/x-2) - (3/x^2-4)/(5/x^2-4) - (2/x+2)

Answer 1

c

Explanation:

(x+2)^2(x-2)

Answer 2

9514 1404 393

Answer:

• common denominator: (x² -4)
• simplified complex fraction: (2x +1)/(9 -2x)

Explanation:

It is helpful to remember the factoring of the difference of squares:

a² -b² = (a -b)(a +b)

__

Your denominator of (x² -4) factors as (x -2)(x +2). You will note that one of these factors is the same as the denominator in the other fraction.

It looks like you want to simplify ...

`(\left((2)/(x-2)-(3)/(x^2-4)\right))/(\left((5)/(x^2-4)-(2)/(x+2)\right))=(\left((2(x+2))/((x-2)(x+2))-(3)/((x-2)(x+2))\right))/(\left((5)/((x-2)(x+2))-(2(x-2))/((x-2)(x+2))\right))\\\\=(2(x+2)-3)/(5-2(x-2))=\boxed{(2x+1)/(9-2x)}`