The expansion of frac{1}{sqrt{4 - 3x}} using | vedclass

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(D) The given expression is $\frac{1}{(4 - 3x)^{1/2}} = (4 - 3x)^{-1/2}$.We can rewrite this as $4^{-1/2} (1 - \frac{3x}{4})^{-1/2} = \frac{1}{2} (1 -

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$-\frac{4}{3} < x < \frac{4}{3}$

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(D) The given expression is $\frac{1}{(4 - 3x)^{1/2}} = (4 - 3x)^{-1/2}$.We can rewrite this as $4^{-1/2} (1 - \frac{3x}{4})^{-1/2} = \frac{1}{2} (1 - \frac{3x}{4})^{-1/2}$.The binomial expansion $(1 - z)^n$ is valid for $|z| Here,$z = \frac{3x}{4}$,so the condition is $|\frac{3x}{4}| This implies $|x| < \frac{4}{3}$,which means $-\frac{4}{3} < x < \frac{4}{3}$.

The expansion of $\frac{1}{\sqrt{4 - 3x}}$ using the binomial theorem is valid if:

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