If a = (frac{2x}{1 – x}) and b = (frac{1 + x}{1 – x}), then a2 – b2 in the simplest form is
-
A.
(frac{3x + 1}{x – 1}) -
B.
(frac{3x^2 – 1}{(x – 1)})2 -
C.
x(frac{3x – 2}{1 – x}) -
D.
(frac{3x^2 – 1}{(x – 1)})
Correct Answer: Option A
Explanation
a2 – b2 = ((frac{2x}{1 – x}))2 – ((frac{1 + x}{1 – x}))2
= ((frac{2x}{1 – x} + frac{1 + x}{1 – x}))((frac{2x}{1 – x} – frac{1 + x}{1 – X}))
= ((frac{3x + 1}{1 – x}))((frac{x – 1}{1 – x}))
= (frac{3x + 1}{x – 1})