Answer:The value of [tex]\frac{x}{2}+\frac{\frac{\frac{x}{3}}{x}}{4}=\frac{3 x+8}{6}[/tex]Solution:
As given the solution is [tex]\frac{x}{2}+\frac{\frac{\frac{x}{3}}{x}}{4}[/tex]Simplifying we get,
[tex]\left(\left(\frac{x}{2}+\left(\frac{\frac{\frac{x}{3}}{x}}{4}\right)\right)\right. \\\\Reciprocal \ of \ \frac{x}{4}[/tex] is \frac{4}{x}
On substituting this we get,
[tex]\left(\frac{x}{2}\right)+\left(\frac{x}{3} \times \frac{4}{x}\right) =\left(\frac{x}{2}\right)+\left(\frac{4 x}{3 x}\right)[/tex][tex]\Rightarrow \frac{x}{2}+\frac{4}{3}[/tex]In order to find the sum, we need common denominator which can be derived by finding the LCM of the given denominators.
Factors of 2: [tex]1\times 2[/tex]Factors of 3: [tex]1\times 3[/tex]Therefore, LCM of 2,3 is 6
[tex]\Rightarrow \frac{x \times 3}{2 \times 3}=\frac{3 x}{6}[/tex][tex]\Rightarrow \frac{4 \times 2}{3 \times 2}=\frac{8}{6}[/tex][tex]\Rightarrow \frac{3 x}{6}+\frac{8}{6}=\frac{3 x+8}{6}[/tex]