Question : If $2x+\frac{1}{3x}$ = 5, then the value of $\frac{5x}{6x^{2}+20x+1}$ is:
Option 1: $\frac{1}{4}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{5}$
Option 4: $\frac{1}{7}$
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Correct Answer: $\frac{1}{7}$
Solution :
Given: $2x+\frac{1}{3x} = 5$
By cross-multiplying,
⇒ $\frac{6x^{2}+1}{3x} = 5$
⇒ $6x^{2} + 1 = 15x$ ------------(i)
Now, $\frac{5x}{6x^{2}+20x+1}$
= $\frac{5x}{15x+20x}$
= $\frac{5x}{35x}$
= $\frac{1}{7}$
Hence, the correct answer is $\frac{1}{7}$.
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