Evaluate
\sqrt{11}+2\approx 5.31662479
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\frac{7\left(\sqrt{11}+2\right)}{\left(\sqrt{11}-2\right)\left(\sqrt{11}+2\right)}
Rationalize the denominator of \frac{7}{\sqrt{11}-2} by multiplying numerator and denominator by \sqrt{11}+2.
\frac{7\left(\sqrt{11}+2\right)}{\left(\sqrt{11}\right)^{2}-2^{2}}
Consider \left(\sqrt{11}-2\right)\left(\sqrt{11}+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{7\left(\sqrt{11}+2\right)}{11-4}
Square \sqrt{11}. Square 2.
\frac{7\left(\sqrt{11}+2\right)}{7}
Subtract 4 from 11 to get 7.
\sqrt{11}+2
Cancel out 7 and 7.
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