Question : If $3x+\frac{1}{5x}=7$, then what is the value of $\frac{5x}{(15x^{2}+15x+1)}?$
Option 1: $\frac{1}{5}$
Option 2: $\frac{1}{10}$
Option 3: $\frac{2}{5}$
Option 4: $10$
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Correct Answer: $\frac{1}{10}$
Solution :
Given: $3x+\frac{1}{5x} =7$
$15x^2 + 1 = 35x$
Adding $15x$ on both sides, we have,
$15x^2 + 15x+1=50x$
Putting this value in the required equation,
$\frac{5x}{(15x^{2}+15x+1)} = \frac{5x}{50x}$
$=\frac{1}{10}$
Hence, the correct answer is $\frac{1}{10}$.
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