To simplify the expression (x² + 12x + 35) / (3x + 15), we need to factor both the numerator and the denominator if possible.
First, let’s factor the numerator:
x² + 12x + 35 can be factored into (x + 5)(x + 7) because 5 and 7 are numbers that multiply to 35 and add up to 12.
Next, we look at the denominator:
3x + 15 can be factored as 3(x + 5). This is because 3 is a common factor of both terms in the denominator.
Now we can rewrite the original expression:
(x + 5)(x + 7) / 3(x + 5)
We see that (x + 5) is a common factor in both the numerator and the denominator. We can cancel this common factor:
(x + 7) / 3
Thus, the simplified expression is:
(x + 7) / 3