What is 1/(sqrt(2)+\sqrt{3)} ?

The solution to 1/(sqrt(2)+\sqrt{3)} is sqrt(3)-sqrt(2)

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simplify 1/(sqrt(2)+\sqrt{3)}

simplify

\frac{1}{2 + 3}

3 - 2

Solution steps

\frac{1}{2 + 3}

Multiply by the conjugate

\frac{2 - 3}{2 - 3}

= \frac{1 \cdot ( 2 - 3 )}{( 2 + 3 ) ( 2 - 3 )}

1 \cdot (2 - 3) = 2 - 3

(2 + 3) (2 - 3) = - 1

= \frac{2 - 3}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

2 - 3 = - (3 - 2)

= \frac{3 - 2}{1}

Apply rule

\frac{a}{1} = a

= 3 - 2

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What is 1/(sqrt(2)+\sqrt{3)} ?
The solution to 1/(sqrt(2)+\sqrt{3)} is sqrt(3)-sqrt(2)