Simplify `(7sqrt3)/(sqrt10+sqrt3)-(2sqrt5)/(sqrt6+sqrt5)-(3sqrt2)/(sqrt15+3sqrt2)`

Explanation

To simplify the expression \(\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}} - \frac{2\sqrt{5}}{\sqrt{6}+\sqrt{5}} - \frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\), we will tackle each term separately and then combine the results.

### Step 1: Simplify the first term \(\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}\)

1. **Rationalize the denominator**:
\[ \frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}} \cdot \frac{\sqrt{10}-\sqrt{3}}{\sqrt{10}-\sqrt{3}} = \frac{7\sqrt{3}(\sqrt{10}-\sqrt{3})}{(\sqrt{10})^2 - (\sqrt{3})^2} \]
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