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: Option 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.