Answer: Third option.
Explanation:
By definition, fractions have the following form:
![(a)/(b)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/4csve9ghyam2nxyvna10u6d4e3rld2pfoh.png)
Where "a" is the Numerator and "b" is the Denominator. Both are Integers and
![b\\eq 0](https://img.qammunity.org/2021/formulas/mathematics/high-school/7n4tlj331wm6prpvgx0xeo6rons35j6xzv.png)
Given the following expression provided in the exercise:
![(x)/(2)+(x)/(5)+(x)/(3)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/dkaj38me2qjmq29nzotddi4jzncrpdj4d1.png)
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:
![LCD=2*5*3\\\\LCD=30](https://img.qammunity.org/2021/formulas/mathematics/middle-school/52g4lhn9kh2d0zfjbh8b0cl8nkb9o4y63d.png)
Step 2. Now you have to divide each original denominator by the LCD and multiply the corresponding numerators by that quotient:
![=(15x+6x+10x)/(30)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qvhw5gyzpcs1i44y9fzp4huqpojyzg8yhw.png)
Step 3. And finally you must solve the addition, getting the following result:
![=(31x)/(30)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/wxmtsuw9zs0kgmmwabmis8efgu2igmvcx5.png)