Question

simplify and answer correctly, if you don't know the answer then pls don't post anything ​

Answer 1

Answer:

After simplifying we will get 0.

Step-by-step explanation:

We have ,

$\sf \dfrac{2}{ \sqrt{5} + \sqrt{3} } + \dfrac{1}{ \sqrt{3} + \sqrt{2} } - \dfrac{3}{ \sqrt{5} + \sqrt{2} }$

• First we will rationalise every term :

$\implies \: \sf \bigg(\dfrac{2 }{ \sqrt{5} + \sqrt{3} } \times \dfrac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \bigg)+ \bigg( \dfrac{1}{ \sqrt{3} + \sqrt{2} } \times \dfrac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \bigg) - \bigg( \dfrac{3}{ \sqrt{5} + \sqrt{2} } \times \dfrac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \bigg)$

• Now solving it :

$\implies \sf \dfrac{2 \times ( \sqrt{5} - \sqrt{3} ) }{ {( \sqrt{5}) }^{2} - {( \sqrt{3} )}^{2} } + \dfrac{ \sqrt{3} - \sqrt{2} }{ ({\sqrt{3}}) ^{2} - (\sqrt{2})^{2} } - \dfrac{3 \times ( \sqrt{5} - \sqrt{2} )}{( \sqrt{5} )^{2} - ( {\sqrt{2} )}^{2}}$

$\implies \sf \dfrac{2 \times ( \sqrt{5} - \sqrt{3} ) }{ 5 - 3 } + \dfrac{ \sqrt{3} - \sqrt{2} }{3 - 2 } - \dfrac{3 \times ( \sqrt{5} - \sqrt{2} )}{5 - 2 }$

$\implies \sf \dfrac{ \cancel{2 } \times ( \sqrt{5} - \sqrt{3} ) }{ \cancel{2} } + \dfrac{ \sqrt{3} - \sqrt{2} }{1} - \dfrac{ \cancel{3} \times ( \sqrt{5} - \sqrt{2} )}{ \cancel{3} }$

$\implies \sf \sqrt{5} - \sqrt{3} + \sqrt{3} - \sqrt{2} - ( \sqrt{5} - \sqrt{2} )$

• Opening the bracket :

$\implies \sf \sqrt{5} - \sqrt{3} + \sqrt{3} - \sqrt{2} - \sqrt{5} + \sqrt{2}$

• All numbers will get cancel :

$\implies \pmb{0}$

Hence, Simplified!

Answer 2

Answer :

Answer after simplification will be 0.

Step-by-step explanation :

According to the question we are given,

$\tt\dfrac{2}{ \sqrt{5} + \sqrt{3} } + \dfrac{1}{ \sqrt{3} + \sqrt{2} } - \dfrac{3}{ \sqrt{5} + \sqrt{2} }$

First let's rationalise each term,

$\tt \longrightarrow \: \bigg(\dfrac{2 }{ \sqrt{5} + \sqrt{3} } \times \dfrac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \bigg)+ \bigg( \dfrac{1}{ \sqrt{3} + \sqrt{2} } \times \dfrac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \bigg) - \bigg( \dfrac{3}{ \sqrt{5} + \sqrt{2} } \times \dfrac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5 - \sqrt{2} } } \bigg)$

Let's start solving!

$\tt \longrightarrow \: \dfrac{2 \times ( \sqrt{5} - \sqrt{3} ) }{ {( \sqrt{5}) }^{2} - {( \sqrt{3} )}^{2} } + \dfrac{ \sqrt{3} - \sqrt{2} }{ ({\sqrt{3}}) ^{2} - (\sqrt{2})^{2} } - \dfrac{3 \times ( \sqrt{5} - \sqrt{2} )}{( \sqrt{5} )^{2} + ( {\sqrt{2} )}^{2}}$

$\tt \longrightarrow \: \dfrac{2 \times ( \sqrt{5} - \sqrt{3} ) }{ 5 - 3 } + \dfrac{ \sqrt{3} - \sqrt{2} }{3 - 2 } - \dfrac{3 \times ( \sqrt{5} - \sqrt{2} )}{5 + 2 }$

$\tt \longrightarrow \: \dfrac{ \cancel{2 } \times ( \sqrt{5} - \sqrt{3} ) }{ \cancel{2} } + \dfrac{ \sqrt{3} - \sqrt{2} }{1} - \dfrac{ \cancel{3} \times ( \sqrt{5} - \sqrt{2} )}{ \cancel{3} }$

• Cancelling some terms and we get,

$\tt \longrightarrow \: \sqrt{5} - \sqrt{3} + \sqrt{3} - \sqrt{2} - ( \sqrt{5} - \sqrt{2} )$

• Now open the brackets,

$\tt \longrightarrow \: \sqrt{5} - \sqrt{3} + \sqrt{3} - \sqrt{2} - \sqrt{5} + \sqrt{2}$

• Numbers which have (-) and (+) and have same value like -√5 and +√5 will get cancelled.

$\tt \longrightarrow \: \cancel{\sqrt{5}}- \cancel{\sqrt{3}} + \cancel{\sqrt{3}} - \cancel{\sqrt{2}} - \cancel{\sqrt{5}} + \cancel{\sqrt{2}}$

$\bf \longrightarrow \: \underline{\boxed{ \bf0}}$

$\bf \longrightarrow \: \underline{\boxed{ \bf \: Hence, Simplified!}}$

Conclusion :-

$\: \: \: \: \: \: \: \: \: \: \bullet \: \sf \: Answer \: = \: \bf0$