Evaluate
\sqrt{11}-\sqrt{7}\approx 0.670873479
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\frac{4\left(\sqrt{11}-\sqrt{7}\right)}{\left(\sqrt{11}+\sqrt{7}\right)\left(\sqrt{11}-\sqrt{7}\right)}
Rationalize the denominator of \frac{4}{\sqrt{11}+\sqrt{7}} by multiplying numerator and denominator by \sqrt{11}-\sqrt{7}.
\frac{4\left(\sqrt{11}-\sqrt{7}\right)}{\left(\sqrt{11}\right)^{2}-\left(\sqrt{7}\right)^{2}}
Consider \left(\sqrt{11}+\sqrt{7}\right)\left(\sqrt{11}-\sqrt{7}\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{4\left(\sqrt{11}-\sqrt{7}\right)}{11-7}
Square \sqrt{11}. Square \sqrt{7}.
\frac{4\left(\sqrt{11}-\sqrt{7}\right)}{4}
Subtract 7 from 11 to get 4.
\sqrt{11}-\sqrt{7}
Cancel out 4 and 4.
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