Question

How do you simplify `(x^2 y^3 + x y^2) / (xy)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(x^2y^3)/(xy) + (xy^2)/(xy)`

Now, cancel common terms in the numerators and denominators:

`(x^(color(red)(cancel(color(black)(2)))1)y^(color(blue)(cancel(color(black)(3)))2))/(color(red)(cancel(color(black)(x)))color(blue)(cancel(color(black)(y)))) + (color(green)(cancel(color(black)(x)))y^(color(purple)(cancel(color(black)(2)))1))/(color(green)(cancel(color(black)(x)))color(purple)(cancel(color(black)(y)))) =>`

`x^1y^2 + y =>`

`xy^2 + y` Where `x != 0` and `y != 0`

Or

`y(xy + 1)` Where `x != 0` and `y != 0`

Answer 2

`color(blue)(=> y(xy +1)`

Explanation:

`(x^2y^3 + x y^2) / (xy)`

`=>( (xy)(xy^2 + y)) / (xy)` taking common term (xy) outside.

`=> (cancel(xy) * (xy^2 + y)) / cancel(xy)`

`=> y(xy +1)` taking “y” outside as common.