152. Simplification. Simplify the expression

$$
\frac{(4+\sqrt{15})^{\frac{3}{2}}+(4-\sqrt{15})^{\frac{3}{2}}}{(6+\sqrt{35})^{\frac{3}{2}}-(6-\sqrt{35})^{\frac{3}{2}}}
$$
152. Multiplying the numerator and the denominator of our fraction by $2 \frac{3}{2}$, we get

$$
\begin{aligned}
\frac{(8+2 \sqrt{15})^{\frac{3}{2}}+(5-2 \sqrt{15}+3)^{\frac{3}{2}}}{(12+2 \sqrt{35})^{\frac{3}{2}}-(7-2 \sqrt{35}+5)^{\frac{3}{2}}} & = \\
\frac{\left(\sqrt{5}+\sqrt{3}^{3}+(\sqrt{5}-\sqrt{3})^{3}\right.}{(\sqrt{7}+\sqrt{5})^{3}-(\sqrt{7}-\sqrt{5})^{3}} & =\frac{2(5 \sqrt{5}+9 \sqrt{5})}{2(21 \sqrt{5}+5 \sqrt{5})}=\frac{7}{13} .
\end{aligned}
$$

$[S . S . M ., \mathbf{5 5}, 567$ (October 1955).]