Answer: The correct option is (B) [tex]\dfrac{2x+1}{2x^2}.[/tex]
Step-by-step explanation: We are given to simplify the following expression :
[tex]E=\dfrac{\dfrac{x}{4}+\dfrac{1}{8}}{\dfrac{x^2}{4}}.[/tex]
We will be using the following property :
[tex]\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\times\dfrac{d}{c}.[/tex]
The simplification is as follows :
[tex]E\\\\\\=\dfrac{\dfrac{x}{4}+\dfrac{1}{8}}{\dfrac{x^2}{4}}\\\\\\=\dfrac{\dfrac{2x+1}{8}}{\dfrac{x^2}{4}}\\\\\\=\dfrac{2x+1}{8}\times \dfrac{4}{x^2}\\\\\\=\dfrac{2x+1}{2x^2}.[/tex]
Thus, the required simplified form of the given expression is [tex]\dfrac{2x+1}{2x^2}.[/tex]
Option (B) is CORRECT.
