If $\frac{2 + 3}{x} = \frac{2 + x}{3}$
What one value for $x$ can be correctly entered into the answer grid?

-5

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-3

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Solution

The correct option is A 3
Given, $\frac{2 + 3}{x} = \frac{2 + x}{3}$
$\Rightarrow 2 x + x^{2} = 15$
$\Rightarrow x^{2} + 2 x - 15 = 0$
$\Rightarrow x^{2} + 5 x - 3 x - 15 = 0$
$\Rightarrow x (x + 5) - 3 (x + 5) = 0$
$\Rightarrow (x + 5) (x - 3) = 0$
$\Rightarrow x = - 5, 3$
Value of $x$ is not negative, so $x = 3$ .

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