# Thread: help finding the common denominator with this rational expression

1. ## help finding the common denominator with this rational expression

4xy/x^2-y^2 + x-y/x+y

im completely lost on this particular problem.

if someone can point me in the correct direction here that would be great, somehow i got 4+x-y/(x-y)^2

2. Originally Posted by NecroWinter
4xy/x^2-y^2 + x-y/x+y

im completely lost on this particular problem.

if someone can point me in the correct direction here that would be great, somehow i got 4+x-y/(x-y)^2
note that the common denominator is $\displaystyle x^2-y^2 = (x+y)(x-y)$

3. $\displaystyle \dfrac{4xy}{x^2-y^2} + \dfrac{x-y}{x+y}$

$\displaystyle = \dfrac{4xy}{(x+y)(x-y)}+ \dfrac{x-y}{x+y}$

$\displaystyle =\dfrac{4xy+(x-y)(x-y)}{(x+y)(x-y)}$

$\displaystyle =\dfrac{4xy+(x-y)^2}{(x+y)(x-y)}$

simplify the numerator..

4. Originally Posted by harish21
$\displaystyle \dfrac{4xy}{x^2-y^2} + \dfrac{x-y}{x+y}$

$\displaystyle = \dfrac{4xy}{(x+y)(x-y)}+ \dfrac{x-y}{x+y}$

$\displaystyle =\dfrac{4xy+(x-y)(x-y)}{(x+y)(x-y)}$

$\displaystyle =\dfrac{4xy+(x-y)^2}{(x+y)(x-y)}$

simplify the numerator..
im a little confused

the only thing i would know to do is to start cancelling things out

when i see (x-y)^2 i assume (x+y)(x-y) and i can cancel out the denom and be left with 4xy.

5. Originally Posted by NecroWinter
im a little confused

the only thing i would know to do is to start cancelling things out

when i see (x-y)^2 i assume (x+y)(x-y) and i can cancel out the denom and be left with 4xy.

numerator ... $\displaystyle 4xy + (x-y)^2 = 4xy + (x^2 - 2xy + y^2) = x^2 + 2xy + y^2 = (x+y)^2$

6. Originally Posted by skeeter
numerator ... $\displaystyle 4xy + (x-y)^2 = 4xy + (x^2 - 2xy + y^2) = x^2 + 2xy + y^2 = (x+y)^2$
thanks i get it now

but i have one more small question

when you have (x-y)^2 how do you know that it isnt a difference of two squares, but rather a perfect square trinomial?

7. Originally Posted by NecroWinter
thanks i get it now

but i have one more small question

when you have (x-y)^2 how do you know that it isnt a difference of two squares, but rather a perfect square trinomial?
a difference of two squares is $\displaystyle x^2 - y^2$ , not $\displaystyle (x-y)^2$ , which is the square of a difference.