Solve (frac{1}{x + 1}) – (frac{1}{x + 3}) = (frac{1}{4})
-
A.
x = -1 or 3 -
B.
x = 1 or 3 -
C.
x = 1 or -5 -
D.
x = -1 or 5 -
E.
x = -1 or -3
Correct Answer: Option C
Explanation
(frac{1}{x + 1}) – (frac{1}{x + 3}) = (frac{1}{4})
(frac{x + 3 – x – 1}{(x + 1)(x + 3)}) = (frac{1}{4})
(frac{2}{x^2 + 4x + 3}) = (frac{1}{4})
= x2 + 4x + 3 = 8
x2 + 4x – 5 = 0
= (x – 1)(x + 5) = 0
x = 1 or -5