Evaluate
9-3\sqrt{5}\approx 2.291796068
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\frac{12\left(3-\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}
Rationalize the denominator of \frac{12}{3+\sqrt{5}} by multiplying numerator and denominator by 3-\sqrt{5}.
\frac{12\left(3-\sqrt{5}\right)}{3^{2}-\left(\sqrt{5}\right)^{2}}
Consider \left(3+\sqrt{5}\right)\left(3-\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{12\left(3-\sqrt{5}\right)}{9-5}
Square 3. Square \sqrt{5}.
\frac{12\left(3-\sqrt{5}\right)}{4}
Subtract 5 from 9 to get 4.
3\left(3-\sqrt{5}\right)
Divide 12\left(3-\sqrt{5}\right) by 4 to get 3\left(3-\sqrt{5}\right).
9-3\sqrt{5}
Use the distributive property to multiply 3 by 3-\sqrt{5}.
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