How do you simplify (2x+7)/(x^2-y^2)+(-5)/(x^2-2xy+y^2)?

1 Answer
May 26, 2018

see below

Explanation:

(2x+7)/(x^2-y^2)+ (-5)/(x^2-2xy+y^2)

firstly factorise the denominators

(2x+7)/((x+y)(x-y))-5/(x-y)^2

we need the denominators the same

multiply top /bottom of first fraction by (x-y)

multiply top/bottom of second fraction by (x+y)

((2x+7)(x-y))/((x+y)(x-y)^2)-(5(x+y))/((x+y)(x-y)^2)

now simplify

(2x^2-2xy+7x-7y-5x-5y)/((x+y)(x-y)^2)

(2x^2-2xy+2x-12y)/((x+y)(x-y)^2)

(2(x^2-xy+x-6y))/((x+y)(x-y)^2)