Question : If $x+\frac{2}{x}=1$, then the value of $\frac{x^2+7x+2}{x^2+13x+2}$ is:
Option 1: $\frac{5}{7}$
Option 2: $\frac{3}{7}$
Option 3: $\frac{4}{7}$
Option 4: $\frac{2}{7}$
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Correct Answer: $\frac{4}{7}$
Solution :
Given: $x+\frac{2}{x}=1$
Now, $\frac{x^2+7 x+2}{x^2+13 x+2}$
Taking $x$ as common from the numerator and the denominator, we get,
$\frac{x(x+7 +\frac{2}{x})}{x(x + 13 + \frac{2}{x})} = \frac{1 + 7}{1 + 13} = \frac{8}{14} = \frac{4}{7}$
Hence, the correct answer is $\frac{4}{7}$.
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