Question

Pls tell the answer fast

Answer 1

Answer:

I thought it would have a clear solution, but that's it:

$x=\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}}-\frac{3\sqrt{3}}{\sqrt{2}+\sqrt{5}}-\frac{2\sqrt{2}}{\sqrt{5}+\sqrt{3}}-\frac{-5\sqrt{3}}{\sqrt{3}}$

$x=\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}}-\frac{3\sqrt{3}}{\sqrt{2}+\sqrt{5}}-\frac{2\sqrt{2}}{\sqrt{5}+\sqrt{3}}-\left(-5\right)$

$x=\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}}-\frac{3\sqrt{3}}{\sqrt{2}+\sqrt{5}}-\frac{2\sqrt{2}}{\sqrt{5}+\sqrt{3}}+5$

The least common multiplier:

$\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)$

$x=\frac{\sqrt{5}\left(\sqrt{10}+\sqrt{6}+5+\sqrt{15}\right)}{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)}-\frac{3\sqrt{3}\left(\sqrt{15}+3+\sqrt{10}+\sqrt{6}\right)}{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)}-\frac{2\sqrt{2}\left(\sqrt{6}+\sqrt{15}+2+\sqrt{10}\right)}{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)}$

$x=\frac{\sqrt{5}\left(\sqrt{10}+\sqrt{6}+5+\sqrt{15}\right)-3\sqrt{3}\left(\sqrt{15}+3+\sqrt{10}+\sqrt{6}\right)-2\sqrt{2}\left(\sqrt{6}+\sqrt{15}+2+\sqrt{10}\right)}{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)}$

$x=\frac{\sqrt{5}\left(5+\sqrt{10}+\sqrt{6}+\sqrt{15}\right)-3\sqrt{3}\left(3+\sqrt{15}+\sqrt{10}+\sqrt{6}\right)-2\sqrt{2}\left(2+\sqrt{6}+\sqrt{15}+\sqrt{10}\right)}{2\sqrt{30}+8\sqrt{2}+7\sqrt{3}+5\sqrt{5}}$

$=\frac{-8\sqrt{2}-4\sqrt{30}-8\sqrt{5}-8\sqrt{3}}{2\sqrt{30}+8\sqrt{2}+7\sqrt{3}+5\sqrt{5}}$

Don't forget that 5

$x=\frac{-8\sqrt{2}-4\sqrt{30}-8\sqrt{5}-8\sqrt{3}}{2\sqrt{30}+8\sqrt{2}+7\sqrt{3}+5\sqrt{5}}+5$