simplify (Class 9th)
Answers
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{3}}\times\frac{\sqrt{6}-\sqrt{3}}{\sqrt{6}-\sqrt{3}}⟹
2
+
3
2
6
×
2
−
3
2
−
3
+
6
+
3
6
2
×
6
−
3
6
−
3
−
6
+
3
8
3
×
6
−
3
6
−
3
\implies\frac{4\sqrt{3}-6\sqrt{2}}{2-3}+\frac{12\sqrt{3}-6\sqrt{6}}{6-3}-\frac{24\sqrt{2}-24}{6-3}⟹
2−3
4
3
−6
2
+
6−3
12
3
−6
6
−
6−3
24
2
−24
\implies\frac{4\sqrt{3}-6\sqrt{2}}{-1}+\frac{12\sqrt{3}-6\sqrt{6}}{3}-\frac{24\sqrt{2}-24}{3}⟹
−1
4
3
−6
2
+
3
12
3
−6
6
−
3
24
2
−24
\implies-4\sqrt{3}+6\sqrt{2}+4\sqrt{3}-2\sqrt{6}-8\sqrt{2}+8⟹−4
3
+6
2
+4
3
−2
6
−8
2
+8
\implies8-2\sqrt{6}-2\sqrt{2}⟹8−2
6
−2
2
Therefore, \frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{3}}=8-2\sqrt{6}-2\sqrt{2}
2
+
3
2
6
+
6
+
3
6
2
−
6
+
3
8
3
=8−2
6
−2
2