Rationalize the denominator and simplify:
\(\frac{a+\sqrt{b}}{\sqrt{b}}\)
To rationalize the denominator, we can multiply both the numerator and the denominator by the conjugate of the denominator.
\[\frac{a+\sqrt{b}}{\sqrt{b}} = \frac{(a+\sqrt{b})(\sqrt{b})}{(\sqrt{b})(\sqrt{b})}\]
\[= \frac{a\sqrt{b} + b}{b}\]
Simplify by dividing both terms by b:
\[= \frac{a\sqrt{b}}{b} + \frac{b}{b}\]
\[= \frac{a\sqrt{b}}{b} + 1\]
Therefore, \(\frac{a+\sqrt{b}}{\sqrt{b}}\) simplifies to \(\frac{a\sqrt{b}}{b} + 1\)