Final answer:
To simplify (5p²)/(5p+2) + (32p+12)/(5p+2), we combine terms over the common denominator and simplify. The resulting expression, (5p² + 32p + 12) / (5p + 2), is in its lowest terms as there are no common factors to cancel.
Step-by-step explanation:
To reduce the expression (5p²)/(5p+2) + (32p+12)/(5p+2) to lowest terms, we can combine the terms since they have the same denominator. The next step is to add the numerators together and then simplify if possible. Let's see the step-by-step process:
Combine the fractions over a common denominator:Simplify the numerator as much as possible. However, in this case, the numerator can't be factored in a way that will cancel any terms with the denominator.The final simplified expression remains (5p² + 32p + 12) / (5p + 2).
There are no common factors between the numerator and denominator that we can cancel out, hence the expression is already in its lowest terms.