Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{ 7 }{ \sqrt{ 5- } \sqrt{ 3 } } + \frac{ 3 }{ \sqrt{ 5 } + \sqrt{ 3 } }$$

Answer

7/(sqrt(5-)*sqrt(3))+(3*(sqrt(5)-sqrt(3)))/2

Solution


Rationalize the denominator: \(\frac{3}{\sqrt{5}+\sqrt{3}} \cdot \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{3\sqrt{5}-3\sqrt{3}}{{\sqrt{5}}^{2}-{\sqrt{3}}^{2}}\).
\[\frac{7}{\sqrt{5-}\sqrt{3}}+\frac{3\sqrt{5}-3\sqrt{3}}{{\sqrt{5}}^{2}-{\sqrt{3}}^{2}}\]
Factor out the common term \(3\).
\[\frac{7}{\sqrt{5-}\sqrt{3}}+\frac{3(\sqrt{5}-\sqrt{3})}{{\sqrt{5}}^{2}-{\sqrt{3}}^{2}}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\frac{7}{\sqrt{5-}\sqrt{3}}+\frac{3(\sqrt{5}-\sqrt{3})}{5-{\sqrt{3}}^{2}}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\frac{7}{\sqrt{5-}\sqrt{3}}+\frac{3(\sqrt{5}-\sqrt{3})}{5-3}\]
Simplify  \(5-3\)  to  \(2\).
\[\frac{7}{\sqrt{5-}\sqrt{3}}+\frac{3(\sqrt{5}-\sqrt{3})}{2}\]
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