Evaluate
\frac{-3\sqrt{5}-3}{4}\approx -2.427050983
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\frac{3\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)}
Rationalize the denominator of \frac{3}{1-\sqrt{5}} by multiplying numerator and denominator by 1+\sqrt{5}.
\frac{3\left(1+\sqrt{5}\right)}{1^{2}-\left(\sqrt{5}\right)^{2}}
Consider \left(1-\sqrt{5}\right)\left(1+\sqrt{5}\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{3\left(1+\sqrt{5}\right)}{1-5}
Square 1. Square \sqrt{5}.
\frac{3\left(1+\sqrt{5}\right)}{-4}
Subtract 5 from 1 to get -4.
\frac{3+3\sqrt{5}}{-4}
Use the distributive property to multiply 3 by 1+\sqrt{5}.
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