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