Evaluate
\frac{9-3\sqrt{7}}{2}\approx 0.531373033
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\frac{3\left(3-\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}
Rationalize the denominator of \frac{3}{3+\sqrt{7}} by multiplying numerator and denominator by 3-\sqrt{7}.
\frac{3\left(3-\sqrt{7}\right)}{3^{2}-\left(\sqrt{7}\right)^{2}}
Consider \left(3+\sqrt{7}\right)\left(3-\sqrt{7}\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(3-\sqrt{7}\right)}{9-7}
Square 3. Square \sqrt{7}.
\frac{3\left(3-\sqrt{7}\right)}{2}
Subtract 7 from 9 to get 2.
\frac{9-3\sqrt{7}}{2}
Use the distributive property to multiply 3 by 3-\sqrt{7}.
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