Evaluate
\frac{85-17\sqrt{3}}{22}\approx 2.525233467
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\frac{17\left(5-\sqrt{3}\right)}{\left(5+\sqrt{3}\right)\left(5-\sqrt{3}\right)}
Rationalize the denominator of \frac{17}{5+\sqrt{3}} by multiplying numerator and denominator by 5-\sqrt{3}.
\frac{17\left(5-\sqrt{3}\right)}{5^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(5+\sqrt{3}\right)\left(5-\sqrt{3}\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{17\left(5-\sqrt{3}\right)}{25-3}
Square 5. Square \sqrt{3}.
\frac{17\left(5-\sqrt{3}\right)}{22}
Subtract 3 from 25 to get 22.
\frac{85-17\sqrt{3}}{22}
Use the distributive property to multiply 17 by 5-\sqrt{3}.
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