A) \[\frac{3}{7}\]
B) \[\frac{4}{9}\]
C) \[\frac{2}{5}\]
D) \[\frac{1}{3}\]
Correct Answer: A
Solution :
Let the numerator be x, then denominator = 2x + 1. Fraction = \[\frac{x}{2x+1}\] Now, \[\Rightarrow \]\[\frac{x}{2x+1}+\frac{2x+1}{x}=\frac{58}{21}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{{{x}^{2}}+4{{x}^{2}}+4x+1}{2{{x}^{2}}+x}=\frac{58}{21}\] \[\Rightarrow \]\[\,11{{x}^{2}}-26x-21=0\] \[\Rightarrow \]\[11{{x}^{2}}-33x+7x-21=0\] \[\Rightarrow \]\[\left( 11x+7 \right)\left( x-3 \right)=0\Rightarrow x=3\] \[\therefore \,\,\,\,\,\,\,\,\,\]The fraction is\[\].
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