Simplify:
$\frac{\sqrt{32} + \sqrt{48}}{\sqrt{8} + \sqrt{12}}$

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Solution

$\sqrt{32} + \sqrt{48} = \sqrt{16 \times 2} + \sqrt{16 \times 3} = 4 (\sqrt{2} + \sqrt{3})$
$\sqrt{8} + \sqrt{12} = \sqrt{4 \times 2} + \sqrt{4 \times 3} = 2 (\sqrt{2} + \sqrt{3})$
$\frac{\sqrt{32} + \sqrt{48}}{\sqrt{8} + \sqrt{12}} = \frac{4 (\sqrt{2} + \sqrt{3})}{2 (\sqrt{2} + \sqrt{3})} = 2$

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