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)#