The value of x+y / x-y + x-y / x+y - 2(x^2 + y^2) / x^2 - y^2 is

Question

The value of \(\frac{x+ y}{x - y} + \frac{x - y}{x + y} - \frac{2(x^2 + y^2)}{x^2 - y^2}\) is:

(a) 1

(b) x

(c) y

(d) 0

Answer 1

Correct option is (d) 0

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

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

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

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

\(= 0\)