Final answer:
To simplify the fraction (9x+12)/15x, divide the numerator and the denominator by their common factor of 3. This results in the simplest form of the fraction being (3x+4)/(5x), with no common factors remaining.
Step-by-step explanation:
To simplify the fraction (9x+12)/15x, we need to factor out the common factors in the numerator and the denominator. First, we look for any common factors between 9x, 12, and 15x. We can see that 3 is a common factor.
Next, we divide both the terms in the numerator by 3:
So the numerator becomes 3x + 4.
The denominator has a 15x, which can also be divided by 3:
Now, our fraction looks like (3x + 4)/(5x).
This is the simplest form since there are no more common factors between the terms in the numerator and the term in the denominator.