Simplify 2/(5 square root of 2-2 square root of 3)

$\frac{2}{5 \sqrt{2} - 2 \sqrt{3}}$

Multiply $\frac{2}{5 \sqrt{2} - 2 \sqrt{3}}$ by $\frac{5 \sqrt{2} + 2 \sqrt{3}}{5 \sqrt{2} + 2 \sqrt{3}}$ .

$\frac{2}{5 \sqrt{2} - 2 \sqrt{3}} \cdot \frac{5 \sqrt{2} + 2 \sqrt{3}}{5 \sqrt{2} + 2 \sqrt{3}}$

Multiply $\frac{2}{5 \sqrt{2} - 2 \sqrt{3}}$ by $\frac{5 \sqrt{2} + 2 \sqrt{3}}{5 \sqrt{2} + 2 \sqrt{3}}$ .

$\frac{2 (5 \sqrt{2} + 2 \sqrt{3})}{(5 \sqrt{2} - 2 \sqrt{3}) (5 \sqrt{2} + 2 \sqrt{3})}$

Expand the denominator using the FOIL method.

$\frac{2 (5 \sqrt{2} + 2 \sqrt{3})}{25 {\sqrt{2}}^{2} + 10 \sqrt{6} - 10 \sqrt{6} - 4 {\sqrt{3}}^{2}}$

Simplify.

$\frac{2 (5 \sqrt{2} + 2 \sqrt{3})}{38}$

Cancel the common factors.

Factor $2$ out of $38$ .

$\frac{2 (5 \sqrt{2} + 2 \sqrt{3})}{2 \cdot 19}$

Cancel the common factor.

$\frac{2 (5 \sqrt{2} + 2 \sqrt{3})}{2 \cdot 19}$

Rewrite the expression.

$\frac{5 \sqrt{2} + 2 \sqrt{3}}{19}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{2} + 2 \sqrt{3}}{19}$

Decimal Form:

$0.55448260 \dots$