What is 7/(-2+sqrt(13)) ?

The solution to 7/(-2+sqrt(13)) is (14+7sqrt(13))/9

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simplify 7/(-2+sqrt(13))

simplify

\frac{7}{- 2 + 13}

\frac{14 + 7 13}{9}

Decimal Notation

4.35987 \dots

Solution steps

\frac{7}{- 2 + 13}

Multiply by the conjugate

\frac{- 2 - 13}{- 2 - 13}

= \frac{7 ( - 2 - 13 )}{( - 2 + 13 ) ( - 2 - 13 )}

Expand

7 (- 2 - 13) : - 14 - 713

Expand

(- 2 + 13) (- 2 - 13) : - 9

= \frac{- 14 - 7 13}{- 9}

\frac{- 14 - 7 13}{- 9} = \frac{14 + 7 13}{9}

= \frac{14 + 7 13}{9}

6 x (2 x - 3) - 5 (2 x^{2} + 9 x - 3)

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11 \cdot (- 1)

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