Question : If $(x+\frac{1}{x})$ = 5, then the value of $\frac{5x}{x^{2}+5x+1}$ is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{2}$
Option 4: $\frac{1}{5}$
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Correct Answer: $\frac{1}{2}$
Solution :
Given:
$(x+\frac{1}{x})$ = 5
⇒ $x^2+1= 5x$
Now, $\frac{5x}{x^{2}+5x+1}$
= $\frac{5x}{x^{2}+1+5x}$
= $\frac{5x}{5x+5x}$
= $\frac{5x}{10x}$
= $\frac{1}{2}$
Hence, the correct answer is $\frac{1}{2}$.
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