Question

Can someone help me simplify this please? `(x^2-y^2)/y^2 xx y^3/(y-x)`

Answer 1

`-y(x+y)`

Explanation:

`x^2-y^2" is a "color(blue)"difference of squares"`

`"and factors in general as"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`rArrx^2-y^2=(x-y)(x+y)`

`rArr((x-y)(x+y))/y^2xxy^3/(y-x)`

`"factor out "-1" from "y-x`

`rArry-x=-(x-y)`

`rArr(cancel((x-y))(x+y))/cancel(y^2)xx(cancel(y^2)y)/-cancel((x-y))`

`=-y(x+y)`