Question 274592
(2-√y)/(3+√y)

To eliminate a radical in the denominator we can multiply both the numerator and denominator by the "conjugate" of the denominator. This is the same a multiplying by 1 so the value of the expression is not changed by doing this. In this case the conjugate of 3+sqrt(y) is 3-sqrt(y) so we have:

[(2-sqrt(y)*(3-sqrt(y)]/[(3+sqrt(y)*(3-sqrt(y))]

Using FOIL above the numerator becomes:

2*3 - 2*sqrt(y) - 3*sqrt(y) + sqrt(y)*sqrt(y) =

6 - 5*sqrt(y) + sqrt(y*y) =

6 - 5*sqrt(y) + y

The denominator becomes:

3*3 - 3 sqrt(y) + 3*sqrt(y) - sqrt(y)*sqrt(y) =

9 - sqrt(y*y) =

9 - y

Putting numerator and denominator together then we have:

(6 - 5*sqrt(y) + y)/(9 - y)