Dividing Fractions
When dividing two fractions, you can flip the second fraction and solve as if they were being multiplied to get your answer
\$\frac{1}{2} \div \frac{2}{1} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\$
Rationalizing the denominator
Rationalizing is the process of multiplying a surd with another similar surd, to result in a rational number. The surd that is used to multiply is called the rationalizing factor (RF).
In math, a conjugate refers to a pair of binomials that have the same terms but opposite signs between them.
Here we can multiply the top and bottom of the fraction by the conjugate to simplify the denomitor
\$\frac{10}{6+\sqrt{5}} * frac{6-\sqrt{5}}{6-\sqrt{5}} =
\frac{10(6-\sqrt{5})}{(6+\sqrt{5})(6-\sqrt{4})} =
\frac{10(6-\sqrt{5})}{36-\sqrt{25}} =
\frac{10(6-\sqrt{5})}{36-5} =
\frac{10(6-\sqrt{5})}{31}\$