Problem 5

Divide x+y by (x2+x*y)/(x-y) and reduce the answer to its lowest terms.

Solution:

a) Replace the division by multiplication by the reciprocal:

(x+y)/(x2+x*y)/(x-y)=(x+y)⋅(x-y)/(x2+x*y)

b) Factor the denominator:

x2+x*y=x*(x+y)

Cancel the common factor x+y ( provided x+y≠0 ):

(x-y)/x

Answer:(x-y)/x