What is 4/(3sqrt(2)+2\sqrt{3)} ?

The solution to 4/(3sqrt(2)+2\sqrt{3)} is (6sqrt(2)-4sqrt(3))/3

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simplify 4/(3sqrt(2)+2\sqrt{3)}

simplify

\frac{4}{3 2 + 2 3}

\frac{6 2 - 4 3}{3}

Decimal Notation

0.51902 \dots

Solution steps

\frac{4}{3 2 + 2 3}

Factor out common term

2 : 2 (3 + 23)

= \frac{4}{2 ( 3 + 2 3 )}

Factor the number:

4 = 2 \cdot 2

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

Apply radical rule:

a = a a

2 = 22

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

Cancel the common factor:

2

= \frac{2 \cdot 2}{3 + 2 3}

23 = 6

= \frac{2 \cdot 2}{3 + 6}

= \frac{2 2}{3 + 6}

Cancel

\frac{2 2}{3 + 6} : \frac{6 2 - 4 3}{3}

= \frac{6 2 - 4 3}{3}

\frac{25}{400}

6 n^{2} - 13 mn - 15 m^{2}

16 - (- 8)

12 x^{2} + 5 x - 7 x^{2}

\frac{10}{70}

What is 4/(3sqrt(2)+2\sqrt{3)} ?
The solution to 4/(3sqrt(2)+2\sqrt{3)} is (6sqrt(2)-4sqrt(3))/3