3 sqrt x - sqrt y / sqrt y + sqrt x #rationalize the denominators

Question

3 sqrt x - sqrt y / sqrt y + sqrt x #rationalize the denominators

Answer 1

Hi Lauren,

Please use parentheses to specify the expressions! I am assuming that the expression is (3 sqrt x - sqrt y) / (sqrt y + sqrt x)

To rationalize the denominator, multiply the expression by the conjugate of the denominator, which is equal to sqrt(y)-sqrt(x)

 

(3 sqrt x - sqrt y) (sqrt(y)-sqrt(x))

-------------------------------------------

(sqrt y + sqrt x) (sqrt(y)-sqrt(x))   (this is equal to the difference of two squares)

 

     (3sqrt(xy) - 3x - y - sqrt(xy))

= ------------------------------------

         y - x   

 

     -3x - y - 2sqrt(xy)

= ------------------------

        y - x

Answer 2

(3√x - √y) / (√y + √x)

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

 

Can you simplify?