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If x + frac 1 x = 5 text &nbsp then...

This question belongs to Arithmetic Ability Algebra
Algebra
?

If $$x + \frac{1}{x} = 5{\text{,}}$$   then the value of $$\frac{{5x}}{{{x^2} + 5x + 1}}$$   is?

Answer & Solution
Correct Answer: Option C
$$\eqalign{ & x + \frac{1}{x} = 5{\text{ then, }}\frac{{5x}}{{{x^2} + 5x + 1}} \cr & \Rightarrow \frac{5}{{x + 5 + \frac{1}{x}}} \cr & \Rightarrow \frac{5}{{x + \frac{1}{x} + 5}} \cr & \Rightarrow \frac{5}{{5 + 5}} \cr & \Rightarrow \frac{1}{2} \cr} $$
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