Question

simplify 2√6/√2+√3 +6√2/√6+√3 -8√3/√6+√2

Answer 1

find the solution in attachment.

Answer 2

Answer:

$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{2}}=0$

Step-by-step explanation:

we have to simplify $\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{2}}$

we simplify each term by rationalizing the denominator of each term

$\implies\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}\times\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}-\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}\times\frac{\sqrt{6}-\sqrt{3}}{\sqrt{6}-\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{2}}\times\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}-\sqrt{2}}$

$\implies\frac{4\sqrt{3}-6\sqrt{2}}{2-3}+\frac{12\sqrt{3}-6\sqrt{6}}{6-3}-\frac{24\sqrt{2}-8\sqrt{6}}{6-2}$

$\implies-4\sqrt{3}+6\sqrt{2}+\frac{12\sqrt{3}-6\sqrt{6}}{3}-\frac{24\sqrt{2}-8\sqrt{6}}{4}$

$\implies-4\sqrt{3}+6\sqrt{2}+4\sqrt{3}-2\sqrt{6}-6\sqrt{2}+2\sqrt{6}$

$\implies-4\sqrt{3}+6\sqrt{2}+4\sqrt{3}-2\sqrt{6}-6\sqrt{2}+2\sqrt{6}$

$\implies0$