What is 1/(2sqrt(2)-3\sqrt{3)} ?

The solution to 1/(2sqrt(2)-3\sqrt{3)} is -(2sqrt(2)+3sqrt(3))/(19)

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simplify 1/(2sqrt(2)-3\sqrt{3)}

simplify

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

- \frac{2 2 + 3 3}{19}

Decimal Notation

- 0.42234 \dots

Solution steps

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

Multiply by the conjugate

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

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

1 \cdot (22 + 33) = 22 + 33

(22 - 33) (22 + 33) = - 19

= \frac{2 2 + 3 3}{- 19}

Apply the fraction rule:

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

= - \frac{2 2 + 3 3}{19}

(x + 5) (x - 5) (x^{2} + 25) (x^{4} + 625) + 6252

9 x - x^{3}

(x + 5) (x - 3)

(1 + i 3)^{6}

\frac{\frac{2 x - 8}{x + 1}}{\frac{3 x ^{2} - 12 x}{x ^{2} - 1}}

What is 1/(2sqrt(2)-3\sqrt{3)} ?
The solution to 1/(2sqrt(2)-3\sqrt{3)} is -(2sqrt(2)+3sqrt(3))/(19)