Prove that $\frac{2 - \sqrt{3}}{5}$ is an irrational number, given that $\sqrt{3}$ is an irrational number.

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Step 1: Assuming $\frac{2 - \sqrt{3}}{5}$ to be a rational number $= \frac{p}{q}$, where $p$ and $q$ are integers and $q 
eq 0$.
Step 2: $\Rightarrow \sqrt{3} = \frac{2q - 5p}{q}$. Here RHS is rational but LHS is irrational.
Step 3: Therefore our assumption is wrong. Hence $\frac{2 - \sqrt{3}}{5}$ is an irrational number.

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