Question

The product of the rational expressions $\frac{x^2-y^2}{x^2+2xy+y^2}and\frac{xy+y^2}{x^2-xy}$ is

• A. $xy$
• B. $\frac{y}{x}$
• C. $\frac{x}{y}$
• D. $1$

Answer 1

The correct option is B $\frac{y}{x}$

Reqd. product = $\frac{x^2-y^2}{x^2+2xy+y^2}\times \frac{xy+y^2}{x^2-xy}$

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