Simplify:
2/√5-√3-1/√3+√2-3/√5-√2
Answers
Answer:
On simplifying we get
Step-by-step explanation:
Given Expression:
we rationalize the denominator of each term of the expression,
Therefore, On simplifying we get
Step-by-step explanation:
Answer:
On simplifying we get \frac{2}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}-\sqrt{2}}=0
5
−
3
2
−
3
+
2
1
−
5
−
2
3
=0
Step-by-step explanation:
Given Expression: \frac{2}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}-\sqrt{2}}
5
−
3
2
−
3
+
2
1
−
5
−
2
3
we rationalize the denominator of each term of the expression,
\implies\frac{2}{\sqrt{5}-\sqrt{3}}\times\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{3}+\sqrt{2}}\times\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}-\frac{3}{\sqrt{5}-\sqrt{2}}\times\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}}⟹
5
−
3
2
×
5
+
3
5
+
3
−
3
+
2
1
×
3
−
2
3
−
2
−
5
−
2
3
×
5
+
2
5
+
2
\implies\frac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}-\frac{1(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}-\frac{3(\sqrt{5}+\sqrt{2})}{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})}⟹
(
5
−
3
)(
5
+
3
)
2(
5
+
3
)
−
(
3
+
2
)(
3
−
2
)
1(
3
−
2
)
−
(
5
−
2
)(
5
+
2
)
3(
5
+
2
)
\implies\frac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5})^2-(\sqrt{3})^2}-\frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3})^2-(\sqrt{2})^2}-\frac{3(\sqrt{5}+\sqrt{2})}{(\sqrt{5})^2-(\sqrt{2})^2}⟹
(
5
)
2
−(
3
)
2
2(
5
+
3
)
−
(
3
)
2
−(
2
)
2
3
−
2
−
(
5
)
2
−(
2
)
2
3(
5
+
2
)
\implies\frac{2(\sqrt{5}+\sqrt{3})}{5-3}-\frac{\sqrt{3}-\sqrt{2}}{3-2}-\frac{3(\sqrt{5}+\sqrt{2})}{5-2}⟹
5−3
2(
5
+
3
)
−
3−2
3
−
2
−
5−2
3(
5
+
2
)
\implies\frac{2(\sqrt{5}+\sqrt{3})}{2}-\frac{\sqrt{3}-\sqrt{2}}{1}-\frac{3(\sqrt{5}+\sqrt{2})}{3}⟹
2
2(
5
+
3
)
−
1
3
−
2
−
3
3(
5
+
2
)
\implies\sqrt{5}+\sqrt{3}-\sqrt{3}+\sqrt{2}-\sqrt{5}-\sqrt{2}⟹
5
+
3
−
3
+
2
−
5
−
2
\implies0⟹0
Therefore, On simplifying we get \frac{2}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}-\sqrt{2}}=0
5
−
3
2
−
3
+
2
1
−
5
−
2
3
=0Answer:
On simplifying we get \frac{2}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}-\sqrt{2}}=0
5
−
3
2
−
3
+
2
1
−
5
−
2
3
=0
Step-by-step explanation:
Given Expression: \frac{2}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}-\sqrt{2}}
5
−
3
2
−
3
+
2
1
−
5
−
2
3
we rationalize the denominator of each term of the expression,
\implies\frac{2}{\sqrt{5}-\sqrt{3}}\times\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{3}+\sqrt{2}}\times\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}-\frac{3}{\sqrt{5}-\sqrt{2}}\times\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}}⟹
5
−
3
2
×
5
+
3
5
+
3
−
3
+
2
1
×
3
−
2
3
−
2
−
5
−
2
3
×
5
+
2
5
+
2
\implies\frac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}-\frac{1(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}-\frac{3(\sqrt{5}+\sqrt{2})}{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})}⟹
(
5
−
3
)(
5
+
3
)
2(
5
+
3
)
−
(
3
+
2
)(
3
−
2
)
1(
3
−
2
)
−
(
5
−
2
)(
5
+
2
)
3(
5
+
2
)
\implies\frac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5})^2-(\sqrt{3})^2}-\frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3})^2-(\sqrt{2})^2}-\frac{3(\sqrt{5}+\sqrt{2})}{(\sqrt{5})^2-(\sqrt{2})^2}⟹
(
5
)
2
−(
3
)
2
2(
5
+
3
)
−
(
3
)
2
−(
2
)
2
3
−
2
−
(
5
)
2
−(
2
)
2
3(
5
+
2
)
\implies\frac{2(\sqrt{5}+\sqrt{3})}{5-3}-\frac{\sqrt{3}-\sqrt{2}}{3-2}-\frac{3(\sqrt{5}+\sqrt{2})}{5-2}⟹
5−3
2(
5
+
3
)
−
3−2
3
−
2
−
5−2
3(
5
+
2
)
\implies\frac{2(\sqrt{5}+\sqrt{3})}{2}-\frac{\sqrt{3}-\sqrt{2}}{1}-\frac{3(\sqrt{5}+\sqrt{2})}{3}⟹
2
2(
5
+
3
)
−
1
3
−
2
−
3
3(
5
+
2
)
\implies\sqrt{5}+\sqrt{3}-\sqrt{3}+\sqrt{2}-\sqrt{5}-\sqrt{2}⟹
5
+
3
−
3
+
2
−
5
−
2
\implies0⟹0
Therefore, On simplifying we get \frac{2}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}-\sqrt{2}}=0
5
−
3
2
−
3
+
2
1
−
5
−
2
3
=0