How to factor this expression

Question

Could someone explain to me the process of factoring this $-6x(x+1)(x^2+2)^{-5/2} + 2(x^2+2)^{-3/2}$ into this $2(1-2x)(x+2)(x^2+2)^{-5/2}$?

Answer 1

Hint Note that $$2(x^2+2)^{-3/2} = 2(x^2 + 2)(x^2+2)^{-5/2}$$

Now factor out $2(x^2+2)^{-5/2}$ from each term.

Answer 2

$$-6x(x+1)(x^2+2)^{-5/2} + 2(x^2+2)^{-3/2}=(x^2+2)^{-\frac{5}{2}}(-6x(x+1)+2(x^2+2)^{-\frac{3}{2}+\frac{5}{2}})$$