<s>[INST] Prove $\frac{(m^2 + 2)(m-1)^2(m+1)^2}{(m^2-1)^{3/2}}=(m^2+2) \sqrt{m^2-1}$ Im trying to get from this expression into:
$$\frac{(m^2 + 2)(m-1)^2(m+1)^2}{(m^2-1)^{3/2}}$$
this expression:
$$(m^2+2) \sqrt{m^2-1}$$
someone know how to do it?
i tried it for hours and can't get from the first expression into the second expression.
please explain to me step by step. I'm newbie.
 [/INST] Write $(m-1)^2(m+1)^2$ as $(m^2-1)^2$.
Then you have $$\frac{(m^2-1)^2}{(m^2-1)^\frac{3}{2}}=\frac{(m^2-1)^\frac{4}{2}}{(m^2-1)^\frac{3}{2}}=(m^2-1)^{\frac{4}{2}-\frac{3}{2}}=(m^2-1)^\frac{1}{2}=\sqrt{m^2-1}$$
The $(m^2+2)$ part stays intact.
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