====== Question 4 Exercise 7.3 ======
Solutions of Question 4 of Exercise 7.3 of Unit 07: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.


Q4 If $x$ is such that $x^2$ and higher of $x$ may be neglected, then show that
$$
\sqrt{\frac{1-3 x}{1+4 x}}=1-\frac{7 x}{2}
$$

Solution: Given that
$$
\sqrt{\frac{1-3 x}{1-4 x}}=(1-3 x)^{\frac{1}{2}}(1+4 x)^{-\frac{1}{2}}
$$

Applying binomial expansion and neglecting $x^2$ and higher powers of $x$.
$$
\begin{aligned}
& =\left(1-\frac{3 x}{2}\right) \times\left(1-\frac{4 x}{2}\right) \\
& =\left(1-\frac{3 x}{2}\right)(1-2 x)
\end{aligned}
$$

Multiplying and neglecting $x^2$ and higher powers of $x$
$$
\begin{aligned}
& =1-2 x-\frac{3 x}{2} \\
& =1 \cdot \frac{4 x+3 x}{2} \\
& =1 \cdot \frac{7 x}{2} .
\end{aligned}
$$






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