Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0
A
\(\frac{1}{x}\)
B
\(\frac{1 - x}{x}\)
C
\(\frac{1 + x}{x}\)
D
\(\frac{1}{x - 1}\)
E
\(\frac{-x - 1}{1}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{1 - x^2}{x - x^2}\), where x = \(\neq\) 0
\(\frac{1^2 - x^2}{x - x^2}\)
= \(\frac{(1 + x)(1 - x)}{x(1 - x)}\)
= \(\frac{1 + x}{x}\)
Source: Myschool Past Questions Archive (Record #32674)