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

1 Answer

Answer:

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

Explanation:

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#