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Evaluate x²(x² - 1)^{-\(\frac{1}{2}...}

Evaluate x²(x² - 1)^{- $\frac{1}{2}$} - (x² - 1)^{$\frac{1}{2}$}

A.

(x² - 1)^{- $\frac{1}{2}$}

B.

(x² - 1)¹

C.

(x² - 1)

D.

(x² - 1)^-1

View answer & explanation

Correct answer is A

x²(x² - 1)^{- $\frac{1}{2}$} - (x² - 1)^{$\frac{1}{2}$} = $\frac{x^2}{(x^2 - 1)^\frac{1}{2}}$ - $\frac{(x^2 - 1)^\frac{1}{2}}{1}$

= $\frac{x^2 - (x^2 - 1)}{(x^2 - 1) ^\frac{1}{2}}$

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

= (x² - 1)^{- $\frac{1}{2}$}

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