JAMB 1990 · UME · Q25

Simplify $\dfrac{x}{x + y} + \dfrac{y}{x - y} - \dfrac{x^2}{x^2 - y^2}$ .

Worked solution (try it first)

The LCD is $x^2 - y^2 = (x + y)(x - y)$ .
Multiply each top by the factor its bottom is missing: $x(x - y) + y(x + y) - x^2$ .
Expand: $x^2 - xy + xy + y^2 - x^2$ .
The $xy$ terms cancel and so do the $x^2$ terms, leaving $y^2$ .
So the expression is $\dfrac{y^2}{x^2 - y^2}$ , option B.