Find the missing numerator \(\frac{5}{x + 1}\) - \(\frac{3}{1 - x}\) - \(\frac{7x - 1}{x^2 - 1}\) = \(\frac{?}{x + 1}\).
A. -1
B. x - 1
C. \(\frac{3(1 - 5x)}{x + 1}\)
D. 1
E. 3(1 - 5x)
Correct Answer: D
Explanation
\(\frac{5}{x + 1} - \frac{3}{1 - x} - \frac{7x - 1}{x^{2} - 1} = \frac{?}{x + 1}\)
\(\frac{5(x - 1) - 3(- (x + 1)) - 7x - 1}{x^{2} - 1}\)
= \(\frac{5x - 5 + 3x + 3 - 7x - 1}{x^{2} - 1}\)
= \(\frac{x - 1}{x^{2} - 1}\)
= \(\frac{x - 1}{(x - 1)(x + 1)}\)
= \(\frac{1}{x + 1}\).
The numerator = 1.
