Simplify? $(3sqrt2-2sqrt3)/(sqrt2+sqrt3)$

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Answer 1 · 2017-03-08T08:26:53

$(3sqrt2-2sqrt3)/(sqrt2+sqrt3)=6/5-sqrt6$

We have (I believe):

$(3sqrt2-2sqrt3)/(sqrt2+sqrt3)$

I'm going to first work with the denominator and rationalize it:

$(3sqrt2-2sqrt3)/(sqrt2+sqrt3)xx(sqrt2-sqrt3)/(sqrt2-sqrt3)$

$((3sqrt2-2sqrt3)(sqrt2-sqrt3))/((sqrt2+sqrt3)(sqrt2-sqrt3))$

$(3sqrt2sqrt2-3sqrt2sqrt3-2sqrt3sqrt2+2sqrt3sqrt3)/(sqrt2sqrt2-sqrt2sqrt3+sqrt2sqrt3+sqrt3sqrt3)$

$((3xx2)-3sqrt6-2sqrt6+(2xx3))/(2+3)$

$(6-5sqrt6+6)/5$

$6/5-sqrt6$

Simplify? (3sqrt2-2sqrt3)/(sqrt2+sqrt3)(3sqrt2-2sqrt3)/(sqrt2+sqrt3)