Answer: Third option.
Step-by-step explanation:
By definition, fractions have the following form:
[tex]\frac{a}{b}[/tex]
Where "a" is the Numerator and "b" is the Denominator. Both are Integers and [tex]b\neq 0[/tex]
Given the following expression provided in the exercise:
[tex]\frac{x}{2}+\frac{x}{5}+\frac{x}{3}[/tex]
You can notice that the denominators of the fractions are different.
Therefore, in order to add the fractions, you can follow the steps shown below:
Step 1. You must find the Least Common Denominator. Since 2, 5 and 3 are Prime numbers, this is:
[tex]LCD=2*5*3\\\\LCD=30[/tex]
Step 2. Now you have to divide each original denominator by the LCD and multiply the corresponding numerators by that quotient:
[tex]=\frac{15x+6x+10x}{30}[/tex]
Step 3. And finally you must solve the addition, getting the following result:
[tex]=\frac{31x}{30}[/tex]
