Question

Simplify the following:

(x^2 - 1)^2 * Sqrt(x + 1)
--------------------
(x - 1)^3/2

Can anyone show me the steps to get to the result: (x + 1)^2 * Sqrt(x^2 - 1)

I can't figure it out.

Answer 1

\[\frac{\left(x^2-1\right)^{2 }(x+1)^{1/2}}{(x-1)^{\frac{3}{2}}}\]
Multiply Top and Bottom by \[(x-1)^{-\frac{3}{2}}\]

Answer 2

\[(x^2 - 1)^2 ==(x+1)^2(x-1)^2\]
\[(x-1)^{-3/2}\left((x+1)^2(x-1)^2(x+1)^{1/2}\right)\]

Answer 3

\[(x+1)^{5/2}(x-1)^2(x-1)^{-3/2}\]
\[(x-1)^{1/2}(x+1)^{5/2}\]