Question

How do you rationalize the denominator and simplify `( 2sqrtx - 3sqrty)/(sqrtx + sqrty)`?

Answer 1

The answer is `=(2x-5sqrt(xy)+3y)/(x-y)`

Explanation:

Let `p=(2sqrtx-3sqrty)/(sqrtx+sqrty)`

Multiply the numerator and denominator by `(sqrtx-sqrty)`

Therefore,

`p=((2sqrtx-3sqrty)((sqrtx-sqrty)))/((sqrtx+sqrty)((sqrtx-sqrty)))`

`=(2x-5sqrt(xy)+3y)/(x-y)`