What is 2 square root x - 3 square root y over square root x plus square root y?

Answer 1

5

Answer 2

That would be an expression with an irrational denominator. You can correct that by multiplying both the numerator and denominator by (√x - √y), giving you a difference of squares on the bottom:

(2√x - 3√y) / (√x + √y)

= [(2√x - 3√y) (√x - √y)] / [ (√x + √y)(√x - √y)]

= (2√x - 3√y) (√x - √y) / (x - y)

And expand the numerator if so desired:

= (2x - 2√[xy] - 3√[xy] + 3y) / (x - y)

= (2x - 5√[xy] + 3y) / (x - y)