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

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The discussion focuses on factoring the complex equation involving terms with exponents of (x-a) and (x+a). The initial suggestion is to factor out (x-a)^(-3/2) as a starting point. However, another participant proposes factoring out (x-a)^(-1/2)(x+a)^(-3/2) instead. This alternative approach aims to simplify the equation further while maintaining the integrity of the original expression. The conversation emphasizes the importance of choosing the correct factor to facilitate easier manipulation of the equation.
mathdad
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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?
 
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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:

$$\frac{1}{2}(x-a)^{-\frac{1}{2}}(x+a)^{-\frac{3}{2}}$$
 
That was my first choice to factor out.
 
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