What is the difference of the rational expressions below?
$\frac{7 x}{x + 4} - \frac{3}{x}$

$\frac{7 x - 3}{x^{2} + 4}$

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$\frac{7 x - 3}{4}$

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$\frac{7 x^{2} - 3 x + 12}{x^{2} + 4 x}$

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$\frac{7 x^{2} - 3 x - 12}{x^{2} + 4 x}$

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Solution

The correct option is D
$\frac{7 x^{2} - 3 x - 12}{x^{2} + 4 x}$

Explanation for the correct option:
We have $\frac{7 x}{x + 4} - \frac{3}{x}$
Taking $L C M$ of the two ratios and subtracting we have,
$\frac{7 x}{x + 4} - \frac{3}{x} = \frac{(7 x) \times x - 3 (x + 4)}{(x + 4) \times x} = \frac{7 x^{2} - 3 x - 12}{x^{2} + 4 x}$
Hence, the correct answer is option $(D)$ .

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