Question

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

Answer 1

The value of
`(x)/(2)+(((x)/(3))/(x))/(4)=(3 x+8)/(6)`

Solution:

As given the solution is
`(x)/(2)+(((x)/(3))/(x))/(4)`

Simplifying we get,

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

On substituting this we get,

`\left((x)/(2)\right)+\left((x)/(3) * (4)/(x)\right) =\left((x)/(2)\right)+\left((4 x)/(3 x)\right)`

`\Rightarrow (x)/(2)+(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* 2`

Factors of 3:
`1* 3`

Therefore, LCM of 2,3 is 6

`\Rightarrow (x * 3)/(2 * 3)=(3 x)/(6)`

`\Rightarrow (4 * 2)/(3 * 2)=(8)/(6)`

`\Rightarrow (3 x)/(6)+(8)/(6)=(3 x+8)/(6)`