How do I rationalize this?

Question

Hi, 

 

Im having difficulty rationalizing this : 

 

(2x—√xy) / (2√xy —(y)) 

Answer 1

To rationalize that you need to multiply by the conjugate of the denominator

(2√xy + y)

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(2x-√xy)((2√xy + y)/(2√xy —y) (2√xy +y) =(4x√xy+2xy-2xy-2√xy)/(4xy-y²)

                                                                                    =(4x√xy-2√xy)/(4xy-y²)
you can factor more if you wan, but that's not necessary.