Question

How do you multiply and simplify `\frac { x ^ { 2} + 2x y + y ^ { 2} } { 2x ^ { 2} + 2x y } \cdot \frac { x - y } { x ^ { 2} - y ^ { 2} }`?

Answer 1

`=1/(2x)`

Explanation:

`(x^2+2xy+y^2)/(2x^2+2xy)times(x-y)/(x^2-y^2)`

`=(x+y)^2/(2x(x+y))times(x-y)/((x+y)(x-y))`

`=(x+y)^2/(2x(x+y)^2)times(x-y)/(x-y)`

`=1/(2x)`