Question
If $$4x + \frac{1}{x} = 5,$$ Â $$x \ne 0{\text{,}}$$ Â then the value of $$\frac{{5x}}{{4{x^2} + 10x + 1}}$$ Â Â is?
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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$$\eqalign{
& \frac{{5x}}{{4{x^2} + 10x + 1}} \cr
& = \frac{5x}{{x\left( {4x + 10 + \frac{1}{x}} \right)}} \cr
& = \frac{5}{{4x + \frac{1}{x} + 10}} \cr
& = \frac{5}{{5 + 10}} \cr
& = \frac{5}{{15}} \cr
& = \frac{1}{3} \cr} $$
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