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

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

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simplify 2/(3-sqrt(7))

simplify

\frac{2}{3 - 7}

3 + 7

Decimal Notation

5.64575 \dots

Solution steps

\frac{2}{3 - 7}

Multiply by the conjugate

\frac{3 + 7}{3 + 7}

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

Expand

2 (3 + 7) : 6 + 27

Expand

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

= \frac{6 + 2 7}{2}

Factor out common term

2 : 2 (3 + 7)

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

Cancel the common factor:

2

= 3 + 7

(- \frac{27}{8})^{\frac{1}{3}}

- 320

- 5 (x + 6) + 7 (x - 4)

(x - 2)^{2} + 5 (x - 2) + 8

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