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

The solution to (sqrt(2)-3)/(sqrt(2)+3) is -(11-6sqrt(2))/7

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simplify (sqrt(2)-3)/(sqrt(2)+3)

simplify

\frac{2 - 3}{2 + 3}

- \frac{11 - 6 2}{7}

Decimal Notation

- 0.35924 \dots

Solution steps

\frac{2 - 3}{2 + 3}

Multiply by the conjugate

\frac{2 - 3}{2 - 3}

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

Expand

(2 - 3) (2 - 3) : 11 - 62

Expand

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

= \frac{11 - 6 2}{- 7}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{11 - 6 2}{7}

\frac{y ^{13}}{y ^{6}}

2 x^{2} = 11 x + 40

a^{2} + 6 a + 9 > 0

- 4 (x + 3) - 0.5 = 11

x^{6} + 3 x^{3} - 4

What is (sqrt(2)-3)/(sqrt(2)+3) ?
The solution to (sqrt(2)-3)/(sqrt(2)+3) is -(11-6sqrt(2))/7