Question

`(5xy-4x^2-y^2)/(x+y)(y^2-x^2)/(y^2-4xy)`?

rational expressions

Answer 1

Given:

`(5xy-4x^2-y^2)/(x+y)(y^2-x^2)/(y^2-4xy) =`

Combine the numerators of the denominators in accordance with the rule of multiplication of fractions::

`((5xy-4x^2-y^2)(y^2-x^2))/((x+y)(y^2-4xy)) =`

Factor:

`((x-y)(y-4x)(x+y)(y-x))/(y(x+y)(y-4x)) =`

Cancel like terms:

`((x-y)cancel((y-4x))cancel((x+y))(y-x))/(ycancel((x+y))cancel((y-4x))) =`

Remove the cancelled terms:

`((x-y)(y-x))/y =`

Multiply the numerator:

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