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

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Answer 1 · 2016-04-22T17:02:57

$= (45+ 9 sqrt6) / ( 19)$

$9 / ( 5 - sqrt6)$

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.

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

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

$= (45+ 9 sqrt6) / ( 25 - 6)$

$= (45+ 9 sqrt6) / ( 19)$

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