How do you simplify 9/(sqrt6 - sqrt5)9√6−√5?

1 Answer
Aleord · MathFact-orials.blogspot.com
Jun 16, 2018

This problem can be solved by using using the conjugate of the denominator and rationalization

Explanation:

\frac{9}{\sqrt{6}-\sqrt{5}} 9√6−√5

=frac{9}{\sqrt{6}-\sqrt{5}} * frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}}=9√6−√5⋅√6+√5√6+√5

=frac{9*(\sqrt{6}+\sqrt{5})}{(\sqrt{6})^2-(\sqrt{5})^2}=9⋅(√6+√5)(√6)2−(√5)2

=frac{9*(\sqrt{6}+\sqrt{5})}{6-5}=9*(\sqrt{6}+\sqrt{5})=9⋅(√6+√5)6−5=9⋅(√6+√5)

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