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If 4x + frac 1 x = 5 &nbsp x ne...

This question belongs to Arithmetic Ability Algebra
Algebra
?

If $$4x + \frac{1}{x} = 5,$$   $$x \ne 0{\text{,}}$$   then the value of $$\frac{{5x}}{{4{x^2} + 10x + 1}}$$    is?

Answer & Solution
Correct Answer: Option B
$$\eqalign{ & \frac{{5x}}{{4{x^2} + 10x + 1}} \cr & = \frac{5x}{{x\left( {4x + 10 + \frac{1}{x}} \right)}} \cr & = \frac{5}{{4x + \frac{1}{x} + 10}} \cr & = \frac{5}{{5 + 10}} \cr & = \frac{5}{{15}} \cr & = \frac{1}{3} \cr} $$
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