simplify (sqrt(5))/(sqrt(6)+2)-2/(5sqrt(3))

⚠ 5sqrt is read as the product 5*sqrt(...): for a power, write 5^sqrt(...)

Let's reduce:

\frac{\sqrt{5}}{\sqrt{6} + 2} - \frac{2}{5 \times \sqrt{3}}

Multiply numerator and denominator by the conjugate

\sqrt{6} - 2

: (a+b)(a-b) = a²-b²

The conventional preference is to have numerical square roots in the numerator rather than in the denominator:

\frac{\sqrt{5} \times (\sqrt{6} - 2)}{2} - \frac{2 \times \sqrt{3}}{3 \times 5}

\frac{\sqrt{5} \times (\sqrt{6} - 2)}{2} - \frac{2 \times \sqrt{3}}{15}

\frac{\sqrt{5} \times \sqrt{6} + \sqrt{5} \times (-2)}{2} - \frac{2 \times \sqrt{3}}{15}

\frac{\sqrt{5 \times 6} - \sqrt{5} \times 2}{2} - \frac{2 \times \sqrt{3}}{15}

\frac{\sqrt{30} - \sqrt{5} \times 2}{2} - \frac{2 \times \sqrt{3}}{15}

▶Simplified form:

\frac{\sqrt{5} \times (\sqrt{6} - 2)}{2} - \frac{2 \times \sqrt{3}}{15}

The numeric value of:

\frac{\sqrt{5} \times (\sqrt{6} - 2)}{2} - \frac{2 \times \sqrt{3}}{15}

equals:

\frac{\approx 2.2361 \times (\approx 2.4495 - 2)}{2} - \frac{2 \times \approx 1.7321}{15}

\frac{\approx 2.2361 \times \approx 0.4495}{2} - \frac{\approx 3.4641}{15}

\frac{\approx 1.0051}{2} - \approx 0.2309

\approx 0.5025 - \approx 0.2309

▷

\approx 0.2716