Question

Simplify the expression.
5x^2/x^2-4 divided by 10x^5/x+2

Which is the correct denominator?

Group of answer choices

(x + 2)(x – 2)

2x^3(x + 2)

5x^3(x – 2)

2x^3(x – 2)

Answer 1

Interpret the expression as (5x^2)/(x^2−4) ÷ (10x^5)/(x+2).

Multiply by the reciprocal:
(5x^2/(x^2−4)) * ((x+2)/(10x^5))
= 5x^2(x+2) / (10x^5(x^2−4))
But x^2−4 = (x−2)(x+2), so cancel (x+2):
= 5x^2 / (10x^5(x−2)) = 1 / (2x^3(x−2)).

Thus the correct denominator is 2x^3(x − 2). (Also note x ≠ 0, ±2.)