MHB Can You Factor Out (x-a)^(-3/2) in This Complex Equation?

[mathdad]

Factor.

I need help getting me started with this monster question.

[(x-a)^(-1/2)]/2 * (x+a)^(-1/2) - [(x+a)^(1/2)]/2 *(x-a)^(-3/2)

Do I factor out (x - a)^(-3/2) as step one?

 

[MarkFL]

We are given to factor:

$$\frac{1}{2}(x-a)^{-\frac{1}{2}}(x+a)^{-\frac{1}{2}}-\frac{1}{2}(x-a)^{\frac{1}{2}}(x+a)^{-\frac{3}{2}}$$

As my first step, I would factor out:

$$\frac{1}{2}(x-a)^{-\frac{1}{2}}(x+a)^{-\frac{3}{2}}$$

 

[mathdad]

That was my first choice to factor out.