Simplifying Equations

Multiply both sides by to get:

Distribute the :

Combine like terms:

Divide both sides by :

Find the common multiple between the numerator and denominator.

divide numerator and denominator by 3:

divide numerator and denominator by 7:

divide numerator and denominator by 4:

Cannot be divided any more- lowest terms.

Divide both sides by :

The mathematical expression given in the question is . Adding together like terms, , this can be simplified to . The expression can be factored as . For every positive integer , must be a multiple of 5. If , then , which is not an integer multiple of 2, 8, 10, or 15. Therefore, the correct answer is 5.