# How do you rationalize the denominator and simplify 9/(5-sqrt6)?

Apr 22, 2016

$= \frac{45 + 9 \sqrt{6}}{19}$

#### Explanation:

$\frac{9}{5 - \sqrt{6}}$

We rationalise the expression by multiplying it with the conjugate of the denominator: color(blue)( 5 + sqrt6

 = ((9 )* (color(blue)(5 + sqrt6))) / (( 5 - sqrt6) * color(blue)((5 + sqrt6))

 = (9 * (color(blue)(5)) + 9 * color(blue)(( sqrt6))) / (( 5 - sqrt6) * color(blue)((5 + sqrt6))

Applying property : color(blue)((a-b)(a+b) = a^2 - b^2 to the denominator.

 = (45+ 9 sqrt6) / (( 5 - sqrt6) * color(blue)((5 + sqrt6))

 = (45+ 9 sqrt6) / (( 5 ^2 - (sqrt6)^2)

$= \frac{45 + 9 \sqrt{6}}{25 - 6}$

$= \frac{45 + 9 \sqrt{6}}{19}$