1/(x+1) - 1/(x - 1) - x^2/(x+1) + x^2/(x - 1), when simplified is equal to :

Question

\(\frac{1}{x+1}-\frac{1}{x-1}-\frac{x^2}{x+1}+\frac{x^2}{x-1},\) when simplified is equal to :

(a) 0 

(b) 1 

(c) 2 

(d) –2

Answer 1

(c) 2

\(\frac{1}{x+1}-\frac{1}{x-1}-\frac{x^2}{x+1}+\frac{x^2}{x-1}\)

= \(\frac{(x-1)-(x+1)-x^2(x-1)+x^2(x+1)}{(x-1)(x+1)}\)

= \(\frac{x-1-x-1-x^3+x^2+x^3+x^2}{x^2-1}\)

= \(\frac{2x^2-2}{x^2-1}=\frac{2(x^2-1)}{(x^2-1)}\) = 2