Rationalize the denominator and simplify: 3+sqrt b/ 3sqrtb
To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator.
Conjugate of 3√b is -3√b:
(3 + √b) / 3√b * (-3√b / -3√b)
= (-3√b(3 + √b)) / 9b
= (-3√b * 3 - 3√b * √b) / 9b
= (-9√b - 3√b^2) / 9b
= (-9√b - 3b) / 9b
Therefore, the simplified form of (3 + √b) / 3√b is (-9√b - 3b) / 9b.