Problem 5

Divide $x+y$ by $\frac{x^2+xy}{x-y}$ and reduce the answer to its lowest terms.

Solution:

a) Replace the division by multiplication by the reciprocal:

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

b) Factor the denominator:

$x^2+xy=x(x+y)$

Cancel the common factor $x+y$ ( provided $x+y\ne 0$ ):

$\frac{x-y}{x}$

Answer:$\frac{x-y}{x}$