Evaluate: (7)/(4-sqrt(11))

Expression: $\frac{ 7 }{ 4-\sqrt{ 11 } }$

Multiply the fraction by $\frac{ 4+\sqrt{ 11 } }{ 4+\sqrt{ 11 } }$

$\frac{ 7 }{ 4-\sqrt{ 11 } } \times \frac{ 4+\sqrt{ 11 } }{ 4+\sqrt{ 11 } }$

To multiply the fractions, multiply the numerators and denominators separately

$\frac{ 7\left( 4+\sqrt{ 11 } \right) }{ \left( 4-\sqrt{ 11 } \right) \times \left( 4+\sqrt{ 11 } \right) }$

Distribute $7$ through the parentheses

$\frac{ 28+7\sqrt{ 11 } }{ \left( 4-\sqrt{ 11 } \right) \times \left( 4+\sqrt{ 11 } \right) }$

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

$\frac{ 28+7\sqrt{ 11 } }{ 16-11 }$

Subtract the numbers

$\begin{align*}&\frac{ 28+7\sqrt{ 11 } }{ 5 } \\&\approx10.24327\end{align*}$