Evaluate: (3)/(sqrt(6)-\sqrt{5)}

Expression: $\frac{ 3 }{ \sqrt{ 6 }-\sqrt{ 5 } }$

Multiply the fraction by $\frac{ \sqrt{ 6 }+\sqrt{ 5 } }{ \sqrt{ 6 }+\sqrt{ 5 } }$

$\frac{ 3 }{ \sqrt{ 6 }-\sqrt{ 5 } } \times \frac{ \sqrt{ 6 }+\sqrt{ 5 } }{ \sqrt{ 6 }+\sqrt{ 5 } }$

To multiply the fractions, multiply the numerators and denominators separately

$\frac{ 3\left( \sqrt{ 6 }+\sqrt{ 5 } \right) }{ \left( \sqrt{ 6 }-\sqrt{ 5 } \right) \times \left( \sqrt{ 6 }+\sqrt{ 5 } \right) }$

Use $\left( a-b \right)\left( a+b \right)={a}^{2}-{b}^{2}$ to simplify the product

$\frac{ 3\left( \sqrt{ 6 }+\sqrt{ 5 } \right) }{ 6-5 }$

Subtract the numbers

$\frac{ 3\left( \sqrt{ 6 }+\sqrt{ 5 } \right) }{ 1 }$

Any expression divided by $1$ remains the same

$3\left( \sqrt{ 6 }+\sqrt{ 5 } \right)$

Distribute $3$ through the parentheses

$\begin{align*}&3\sqrt{ 6 }+3\sqrt{ 5 } \\&\approx14.05667\end{align*}$