How do you rationalize the denominator and simplify $3/(2-sqrt6)$ ?

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Answer 1 · 2016-06-16T10:42:41

$3/(2-sqrt6)=-3-3/2sqrt6$

To rationalize denominator and simplify $3/(2-sqrt6)$ ,

one should multiply numerator and denominator of the fraction by conjugate irrational number of denominator $2-sqrt6$ , which is $2+sqrt6$ .

Hence $3/(2-sqrt6)=3/(2-sqrt6)xx(2+sqrt6)/(2+sqrt6)$

= $(3(2+sqrt6))/((2-sqrt6)(2+sqrt6))$

= $(6+3sqrt6)/(2^2-(sqrt6)^2)$

= $(6+3sqrt6)/(4-6)$

= $(6+3sqrt6)/(-2)$

= $-3-3/2sqrt6$

How do you rationalize the denominator and simplify 3/(2-sqrt6)3/(2-sqrt6)?