How do you simplify (2x+7)/(x^2-y^2)+(-5)/(x^2-2xy+y^2)2x+7x2y2+5x22xy+y2?

1 Answer
May 26, 2018

see below

Explanation:

(2x+7)/(x^2-y^2)+ (-5)/(x^2-2xy+y^2)2x+7x2y2+5x22xy+y2

firstly factorise the denominators

(2x+7)/((x+y)(x-y))-5/(x-y)^22x+7(x+y)(xy)5(xy)2

we need the denominators the same

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

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

((2x+7)(x-y))/((x+y)(x-y)^2)-(5(x+y))/((x+y)(x-y)^2)(2x+7)(xy)(x+y)(xy)25(x+y)(x+y)(xy)2

now simplify

(2x^2-2xy+7x-7y-5x-5y)/((x+y)(x-y)^2)2x22xy+7x7y5x5y(x+y)(xy)2

(2x^2-2xy+2x-12y)/((x+y)(x-y)^2)2x22xy+2x12y(x+y)(xy)2

(2(x^2-xy+x-6y))/((x+y)(x-y)^2)2(x2xy+x6y)(x+y)(xy)2