Simplify the numerator sqrt(48).

You're on a roll — Step 1: Simplify the numerator $\sqrt{48}$. We find the largest perfect square factor of 48. $\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$

Step 2: Rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator, which is $\sqrt{5} - \sqrt{3}$. $\frac{4\sqrt{3}}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}}$

Step 3: Expand the numerator and the denominator. For the numerator: $4\sqrt{3}(\sqrt{5} - \sqrt{3}) = 4\sqrt{3} \times \sqrt{5} - 4\sqrt{3} \times \sqrt{3} = 4\sqrt{15} - 4 \times 3 = 4\sqrt{15} - 12$ For the denominator, use the difference of squares formula $(x+y)(x-y) = x^2 - y^2$: $(\sqrt{5} + \sqrt{3})(\sqrt{5} - \sqrt{3}) = (\sqrt{5})^2 - (\sqrt{3})^2 = 5 - 3 = 2$

Step 4: Combine the simplified numerator and denominator. $\frac{4\sqrt{15} - 12}{2}$

Step 5: Divide each term in the numerator by the denominator. $\frac{4\sqrt{15}}{2} - \frac{12}{2} = 2\sqrt{15} - 6$

The expression is in the form $a\sqrt{b} + c$, where $a=2$, $b=15$, and $c=-6$.

The simplified expression is $\boxed{2\sqrt{15} - 6}$.

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