Question

divide.
$\frac{3b^{2}+23b+30}{3b+5}$

Explanation:

Step1: Factor the numerator

We factor $3b^2 + 23b + 30$. We need two numbers that multiply to $3\times30=90$ and add to 23. These numbers are 18 and 5.
$$3b^2 + 18b + 5b + 30 = 3b(b+6) + 5(b+6) = (3b+5)(b+6)$$

Step2: Cancel common factors

The numerator is $(3b+5)(b+6)$ and the denominator is $3b+5$ (where $3b+5
eq0$). Cancel the common factor $3b+5$.
$$\frac{(3b+5)(b+6)}{3b+5} = b+6$$

Answer:

$b + 6$ (where $b
eq -\frac{5}{3}$)