Evaluate
\frac{-\sqrt{15}-1}{2}\approx -2.436491673
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\frac{7\left(1+\sqrt{15}\right)}{\left(1-\sqrt{15}\right)\left(1+\sqrt{15}\right)}
Rationalize the denominator of \frac{7}{1-\sqrt{15}} by multiplying numerator and denominator by 1+\sqrt{15}.
\frac{7\left(1+\sqrt{15}\right)}{1^{2}-\left(\sqrt{15}\right)^{2}}
Consider \left(1-\sqrt{15}\right)\left(1+\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(1+\sqrt{15}\right)}{1-15}
Square 1. Square \sqrt{15}.
\frac{7\left(1+\sqrt{15}\right)}{-14}
Subtract 15 from 1 to get -14.
-\frac{1}{2}\left(1+\sqrt{15}\right)
Divide 7\left(1+\sqrt{15}\right) by -14 to get -\frac{1}{2}\left(1+\sqrt{15}\right).
-\frac{1}{2}-\frac{1}{2}\sqrt{15}
Use the distributive property to multiply -\frac{1}{2} by 1+\sqrt{15}.
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