Evaluate
\frac{-9\sqrt{15}-72}{49}\approx -2.180752043
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\frac{-9\left(8+\sqrt{15}\right)}{\left(8-\sqrt{15}\right)\left(8+\sqrt{15}\right)}
Rationalize the denominator of \frac{-9}{8-\sqrt{15}} by multiplying numerator and denominator by 8+\sqrt{15}.
\frac{-9\left(8+\sqrt{15}\right)}{8^{2}-\left(\sqrt{15}\right)^{2}}
Consider \left(8-\sqrt{15}\right)\left(8+\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{-9\left(8+\sqrt{15}\right)}{64-15}
Square 8. Square \sqrt{15}.
\frac{-9\left(8+\sqrt{15}\right)}{49}
Subtract 15 from 64 to get 49.
\frac{-72-9\sqrt{15}}{49}
Use the distributive property to multiply -9 by 8+\sqrt{15}.
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