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

The correct option is D 0

$\frac{x+y}{x-y}+\frac{x-y}{x+y}-\frac{2(x^2+y^2)}{x^2-y^2}$
$\Rightarrow \frac{(x+y)(x+y)+(x-y)(x-y)-2(x^2+y^2)}{x^2-y^2}$
$\Rightarrow \frac{x^2+y^2+2xy+x^2+y^2-2xy-2(x^2+y^2)}{x^2-y^2}$
$\Rightarrow \frac{x^2+y^2+2xy+x^2+y^2-2xy-2x^2-2y^2}{x^2-y^2}$
$\Rightarrow \frac{0}{x^2-y^2}=0$