Question

Simplify x/2 + x/3 /x/4=

Answer 1

    6x + 1

 ——————

       12  

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Answer 2

Answer:

The value of  $\frac{x}{2}+\frac{\frac{\frac{x}{3}}{x}}{4}=\frac{3 x+8}{6}$

Solution:

As given the solution is $\frac{x}{2}+\frac{\frac{\frac{x}{3}}{x}}{4}$

Simplifying we get,

$\left(\left(\frac{x}{2}+\left(\frac{\frac{\frac{x}{3}}{x}}{4}\right)\right)\right. \\\\Reciprocal \ of \ \frac{x}{4}$ is \frac{4}{x}

On substituting this we get,

$\left(\frac{x}{2}\right)+\left(\frac{x}{3} \times \frac{4}{x}\right) =\left(\frac{x}{2}\right)+\left(\frac{4 x}{3 x}\right)$

$\Rightarrow \frac{x}{2}+\frac{4}{3}$

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: $1\times 2$

Factors of 3: $1\times 3$

Therefore, LCM of 2,3 is 6

$\Rightarrow \frac{x \times 3}{2 \times 3}=\frac{3 x}{6}$

$\Rightarrow \frac{4 \times 2}{3 \times 2}=\frac{8}{6}$

$\Rightarrow \frac{3 x}{6}+\frac{8}{6}=\frac{3 x+8}{6}$