x^3+5x^2-xy-5y/2x^3-2xy+x^2-y

Question

simplify- x^3+5x^2-xy-5y/2x^3-2xy+x^2-y

 

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Answer 1

x³+5x²-xy-5y=x²(x+5)-y(x+5)=(x²-y)(x+5); 

2x³-2xy+x²-y=2x(x²-y)+x²-y=(2x+1)(x²-y).

So x²-y is a common factor for the denominator and numerator and this common factor cancels out leaving:

(x+5)/(2x+1).