What is 3/(2+sqrt(7)) ?

The solution to 3/(2+sqrt(7)) is -2+sqrt(7)

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simplify 3/(2+sqrt(7))

simplify

\frac{3}{2 + 7}

- 2 + 7

Decimal Notation

0.64575 \dots

Solution steps

\frac{3}{2 + 7}

Multiply by the conjugate

\frac{2 - 7}{2 - 7}

= \frac{3 ( 2 - 7 )}{( 2 + 7 ) ( 2 - 7 )}

Expand

3 (2 - 7) : 6 - 37

Expand

(2 + 7) (2 - 7) : - 3

= \frac{6 - 3 7}{- 3}

Factor out common term

3 : 3 (2 - 7)

= \frac{3 ( 2 - 7 )}{- 3}

Cancel the common factor:

3

= \frac{2 - 7}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (2 - 7)

- (2 - 7) = - 2 + 7

= - 2 + 7

(- (2 - x)^{\frac{1}{2}})^{2}

8 e^{- \frac{πi}{6}}

(2 + 3)^{3}

\frac{f}{f + 3} - \frac{3}{f + 3}

\frac{9 - x ^{2}}{3 + x}