how do i solve this? 4√(x) over x+2√(y)

Question

I am suppose to rationalize the denominator and simplify. I have tried...and somehow I just couldn't get the right aswer. I just need to be reminded how to do it. Thanks!

Answer 1

Rationalize the denominator.  Hm.

You know how something like (x+1)(x-1) makes x^2 - 1 with no x term in the middle?  Like that.

multiply the top and bottom by x-2Sqrt(y)

4( Sqrt(x) )(x - 2Sqrt(y) ) / (x + 2Sqrt(y) )(x - 2Sqrt(y) )

multiply the bottom parts together

4( Sqrt(x) )(x - 2Sqrt(y) ) / (x^2 - 4y)

if you want, multiply the tops together too

4(x^3/2 - 2Sqrt(xy) ) / (x^2 - 4y)

or even

(4x^3/2 - 8Sqrt(xy) ) / (x^2 - 4y)