The value of

is:

Simplify the roots within both sections step by step:
For the Numerator components:

$$\sqrt{32}=\sqrt{16\times 2}=4\sqrt{2}$$

$$\sqrt{48}=\sqrt{16\times 3}=4\sqrt{3}$$

$$\text{Numerator}=4\sqrt{2}+4\sqrt{3}=4(\sqrt{2}+\sqrt{3})$$

For the Denominator components:

$$\sqrt{8}=\sqrt{4\times 2}=2\sqrt{2}$$

$$\sqrt{12}=\sqrt{4\times 3}=2\sqrt{3}$$

$$\text{Denominator}=2\sqrt{2}+2\sqrt{3}=2(\sqrt{2}+\sqrt{3})$$

Combining both expressions:

$$\text{Value}=\frac{4(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}=\frac{4}{2}=2$$