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

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Answer 1 · 2018-05-26T08:23:08

see below

#(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)#