Home » Mathematics » Evaluate x2(x2 – 1)-(frac{1}{2}) – (x2 – 1)(frac{1}{2})

Evaluate x2(x2 – 1)-(frac{1}{2}) – (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

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})}