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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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)-\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #31413)