Question

Simplify:- help me by solvin this question​

Answer 1

Hope this helped you.....if there is any problem so pls comment

Answer 2

Answer:

The simplified value of the given expression is $\boxed{\bf 0}$.

Step-by-step explanation:

The given problem is based on the concept of rationalization.

Consider that the given expression is expressed as shown below:

$\boxed{\text{A}=\dfrac{1}{\sqrt{3}+\sqrt{2}}-\dfrac{2}{\sqrt{5}-\sqrt{3}}-\dfrac{3}{\sqrt{2}-\sqrt{5}}}$

Solve the above expression as shown below:

$\begin{aligned}\text{A}&=\dfrac{1}{\sqrt{3}+\sqrt{2}}-\dfrac{2}{\sqrt{5}-\sqrt{3}}-\dfrac{3}{\sqrt{2}-\sqrt{5}}\\&=\left(\dfrac{1}{\sqrt{3}+\sqrt{2}}\times\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}\right)-\left(\dfrac{2}{\sqrt{5}-\sqrt{3}}\times\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}\right)-\left(\dfrac{3}{\sqrt{2}-\sqrt{5}}\times\dfrac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}}\right)\end{aligned}$

Further solve the above expression as shown below:

$\begin{aligned}\text{A}&=\dfrac{\sqrt{3}-\sqrt{2}}{3-2}-\dfrac{2\times \left(\sqrt{5}+\sqrt{3}\right)}{5-3}-\dfrac{3\times \left(\sqrt{2}+\sqrt{5}\right)}{2-5}\\&=\sqrt{3}-\sqrt{2}-\left(\sqrt{5}+\sqrt{3}\right)+\sqrt{2}+\sqrt{5}\\&=\sqrt{3}-\sqrt{2}-\sqrt{5}-\sqrt{3}+\sqrt{2}+\sqrt{5}\\&=\left(\sqrt{3}-\sqrt{3}\right)+\left(\sqrt{2}-\sqrt{2}\right)+\left(\sqrt{5}-\sqrt{5}\right)\\&=0\end{aligned}$

Therefore, the simplified value of the given expression is $\boxed{\bf 0}$.