\[\frac{\sqrt{10}-\sqrt{3}}{\sqrt{10}+\sqrt{3}}\]
1
Rationalize the denominator: 10−310+3⋅10−310−3=10−30−30+3102−32\frac{\sqrt{10}-\sqrt{3}}{\sqrt{10}+\sqrt{3}} \cdot \frac{\sqrt{10}-\sqrt{3}}{\sqrt{10}-\sqrt{3}}=\frac{10-\sqrt{30}-\sqrt{30}+3}{{\sqrt{10}}^{2}-{\sqrt{3}}^{2}}.
10−30−30+3102−32\frac{10-\sqrt{30}-\sqrt{30}+3}{{\sqrt{10}}^{2}-{\sqrt{3}}^{2}}

2
Collect like terms.
(10+3)+(−30−30)102−32\frac{(10+3)+(-\sqrt{30}-\sqrt{30})}{{\sqrt{10}}^{2}-{\sqrt{3}}^{2}}

3
Simplify  (10+3)+(−30−30)(10+3)+(-\sqrt{30}-\sqrt{30})  to  13−23013-2\sqrt{30}.
13−230102−32\frac{13-2\sqrt{30}}{{\sqrt{10}}^{2}-{\sqrt{3}}^{2}}

4
Use this rule: x2=x{\sqrt{x}}^{2}=x.
13−23010−32\frac{13-2\sqrt{30}}{10-{\sqrt{3}}^{2}}

5
Use this rule: x2=x{\sqrt{x}}^{2}=x.
13−23010−3\frac{13-2\sqrt{30}}{10-3}

6
Simplify  10−310-3  to  77.
13−2307\frac{13-2\sqrt{30}}{7}

Done

Decimal Form: 0.292221
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