What is 4/(6+sqrt(10)) ?

The solution to 4/(6+sqrt(10)) is (2(6-sqrt(10)))/(13)

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simplify 4/(6+sqrt(10))

simplify

\frac{4}{6 + 10}

\frac{2 ( 6 - 10 )}{13}

Decimal Notation

0.43657 \dots

Solution steps

\frac{4}{6 + 10}

Multiply by the conjugate

\frac{6 - 10}{6 - 10}

= \frac{4 ( 6 - 10 )}{( 6 + 10 ) ( 6 - 10 )}

Expand

4 (6 - 10) : 24 - 410

Expand

(6 + 10) (6 - 10) : 26

= \frac{24 - 4 10}{26}

Factor out common term

4 : 4 (6 - 10)

= \frac{4 ( 6 - 10 )}{26}

Factor the number:

4 = 2 \cdot 2

= \frac{2 \cdot 2 ( 6 - 10 )}{26}

Factor the number:

26 = 2 \cdot 13

= \frac{2 \cdot 2 ( 6 - 10 )}{2 \cdot 13}

Cancel the common factor:

2

= \frac{2 ( 6 - 10 )}{13}

3 x^{2} - 2 x y - y^{2}

- x^{3} + x^{2} + 12 x

- (x - 1) (x - 1)

64%