What is the difference between the rational expressions below?
$\frac{9}{x^{2}} - \frac{2 x + 1}{8 x}$

$\frac{- 2 x^{2} + x + 72}{8 x^{2}}$

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$\frac{- 2 x + 10}{8 x^{2}}$

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$\frac{- 2 x^{2} - x + 72}{8 x^{2}}$

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$\frac{- 2 x + 8}{8 x^{2}}$

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Solution

The correct option is C
$\frac{- 2 x^{2} - x + 72}{8 x^{2}}$

Explanation for the correct option.
Difference between the rational expressions.
We have, $\frac{9}{x^{2}} - \frac{2 x + 1}{8 x}$
Making the denominator equal,
$= \frac{8 \times 9}{8 x^{2}} - \frac{(2 x + 1) x}{8 x (x)} = \frac{72}{8 x^{2}} - \frac{2 x^{2} + x}{8 x^{2}} = \frac{- 2 x^{2} - x + 72}{8 x^{2}}$
Hence, the correct answer is option (C).

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