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

- 4.64575 \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

\frac{5.6}{8} \cdot (x + 8) = \frac{6}{12} \cdot (x + 12)

7 (m + 9) - 18 = 59

8 x^{2} + 22 x = 21

4 x^{2} - 2 x + 8 = 0

16 x^{4} + 56 x^{2} + 49