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

The solution to (sqrt(2))/(sqrt(7)+2) is (sqrt(14)-2sqrt(2))/3

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

simplify

\frac{2}{7 + 2}

\frac{14 - 2 2}{3}

Solution steps

\frac{2}{7 + 2}

Multiply by the conjugate

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

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

Expand

2 (7 - 2) : 14 - 22

Expand

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

= \frac{14 - 2 2}{3}

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

(- x^{2} - 2 x - 2) (- 2 x^{2} + 7 x + 1)

\frac{4 ab}{6 a}

\frac{4992000}{858000000}

19 x^{13}

What is (sqrt(2))/(sqrt(7)+2) ?
The solution to (sqrt(2))/(sqrt(7)+2) is (sqrt(14)-2sqrt(2))/3