$\frac{ 7 }{ 4-\sqrt{ 11 } } \times \frac{ 4+\sqrt{ 11 } }{ 4+\sqrt{ 11 } }$
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$\begin{align*}&\frac{ 28+7\sqrt{ 11 } }{ 5 } \\&\approx10.24327\end{align*}$