What is rationalize 3/(1+sqrt(2)) ?

The solution to rationalize 3/(1+sqrt(2)) is -3(1-sqrt(2))

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rationalize 3/(1+sqrt(2))

rationalize

\frac{3}{1 + 2}

- 3 (1 - 2)

Decimal Notation

1.24264 \dots

Solution steps

\frac{3}{1 + 2}

Multiply by the conjugate

\frac{1 - 2}{1 - 2}

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

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

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= - 3 (1 - 2)

\frac{3 x ^{4} + 6 x}{2 x ^{4} + x ^{3} + 4 x + 2}

(- 2 + 2)^{e}

4 x^{2} - y^{2} - 2 x + y

\frac{2 i}{1 + 7 i}

(5 n + 8)^{2}

What is rationalize 3/(1+sqrt(2)) ?
The solution to rationalize 3/(1+sqrt(2)) is -3(1-sqrt(2))