Rationalize the denominator and simplify: sqrt 5/ a-sqrt 5
To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator.
The conjugate of a - sqrt(5) is a + sqrt(5).
(sqrt(5))/(a - sqrt(5)) * (a + sqrt(5))/(a + sqrt(5))
= (sqrt(5)(a + sqrt(5)))/(a^2 - 5)
= (sqrt(5)a + 5)/(a^2 - 5)
Therefore, the rationalized and simplified form of sqrt(5)/(a - sqrt(5)) is (sqrt(5)a + 5)/(a^2 - 5).