How do you simplify $1/(sqrt2+sqrt3)$ ?

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Answer 1 · 2016-02-27T05:19:56

Multiply the denominator with $sqrt3-sqrt2$ to get

$(sqrt3-sqrt2)/[(sqrt3+sqrt2)*(sqrt3-sqrt2)]= (sqrt3-sqrt2)/((sqrt3)^2-(sqrt2)^2)= (sqrt3-sqrt2)/(1)=sqrt3-sqrt2$

Answer 2 · 2018-03-01T23:39:13

$(1)/(sqrt2+sqrt3)=color(blue)(sqrt3-sqrt2$

Simplify:

$(1)/(sqrt2+sqrt3)$

Rationalize the denominator.

$(1)/(sqrt2+sqrt3)xx(sqrt2-sqrt3)/(sqrt2-sqrt3)$

Simplify.

$(sqrt2-sqrt3)/(sqrt(2)^2-sqrt(3)^2)$

Apply rule: $sqrt(x)^2=x$ .

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

Simplify.

$(sqrt2-sqrt3)/(-1)$

Simplify.

$-(sqrt2-sqrt3)$

Simplify parentheses.

$-sqrt2+sqrt3=$

$sqrt3-sqrt2$

How do you simplify 1/(sqrt2+sqrt3)1/(sqrt2+sqrt3)?