Evaluate
\frac{-1189\sqrt{6}-20213}{283}\approx -81.715347365
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\frac{1189}{\sqrt{6}-17}
Subtract 16 from 1205 to get 1189.
\frac{1189\left(\sqrt{6}+17\right)}{\left(\sqrt{6}-17\right)\left(\sqrt{6}+17\right)}
Rationalize the denominator of \frac{1189}{\sqrt{6}-17} by multiplying numerator and denominator by \sqrt{6}+17.
\frac{1189\left(\sqrt{6}+17\right)}{\left(\sqrt{6}\right)^{2}-17^{2}}
Consider \left(\sqrt{6}-17\right)\left(\sqrt{6}+17\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{1189\left(\sqrt{6}+17\right)}{6-289}
Square \sqrt{6}. Square 17.
\frac{1189\left(\sqrt{6}+17\right)}{-283}
Subtract 289 from 6 to get -283.
\frac{1189\sqrt{6}+20213}{-283}
Use the distributive property to multiply 1189 by \sqrt{6}+17.
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