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Rewrite the expression using exponent rules.

May 14, 2026Mathematics

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Here's the solution for Item 5:

a) Obtain the range of values of $x$ for which the machine considers the expansion of $\sqrt{\frac{1+3x}{1-3x}}$ as valid.

Rewrite the expression using exponent rules.
$\sqrt{\frac{1+3x}{1-3x}} = (1+3x)^{1/2} (1-3x)^{-1/2}$
Determine the validity range for each binomial expansion.
For a binomial expansion $(1+u)^n$ to be valid, the condition is $|u| < 1$ .
For $(1+3x)^{1/2}$ , we need $|3x| < 1$ , which