Evaluate
\frac{7\left(\sqrt{15}+2\right)}{11}\approx 3.737353038
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\frac{-7\left(2+\sqrt{15}\right)}{\left(2-\sqrt{15}\right)\left(2+\sqrt{15}\right)}
Rationalize the denominator of \frac{-7}{2-\sqrt{15}} by multiplying numerator and denominator by 2+\sqrt{15}.
\frac{-7\left(2+\sqrt{15}\right)}{2^{2}-\left(\sqrt{15}\right)^{2}}
Consider \left(2-\sqrt{15}\right)\left(2+\sqrt{15}\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(2+\sqrt{15}\right)}{4-15}
Square 2. Square \sqrt{15}.
\frac{-7\left(2+\sqrt{15}\right)}{-11}
Subtract 15 from 4 to get -11.
\frac{-14-7\sqrt{15}}{-11}
Use the distributive property to multiply -7 by 2+\sqrt{15}.
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