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

Mathematics

JAMB 1991

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

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Correct Answer: Option A

Explanation

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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