What is 9/(2sqrt(7)+1) ?

The solution to 9/(2sqrt(7)+1) is (2sqrt(7)-1)/3

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simplify 9/(2sqrt(7)+1)

simplify

\frac{9}{2 7 + 1}

\frac{2 7 - 1}{3}

Solution steps

\frac{9}{2 7 + 1}

Multiply by the conjugate

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

= \frac{9 ( 2 7 - 1 )}{( 2 7 + 1 ) ( 2 7 - 1 )}

Expand

9 (27 - 1) : 187 - 9

Expand

(27 + 1) (27 - 1) : 27

= \frac{18 7 - 9}{27}

Factor out common term

9 : 9 (27 - 1)

= \frac{9 ( 2 7 - 1 )}{27}

Factor the number:

27 = 9 \cdot 3

= \frac{9 ( 2 7 - 1 )}{9 \cdot 3}

Cancel the common factor:

9

= \frac{2 7 - 1}{3}

5 \cdot 0. 1^{1} \cdot (0.9)^{4}

31 + 31

1 + 2 x - 3 x^{2}

8 c + 3 - 2 c + 7

- 5 \times 9