## Simplifying the Expression (5ab - 10b² + 15bc) ÷ 5b

This expression involves dividing a trinomial by a monomial. Let's break down the steps to simplify it:

**1. Understanding the Process**

When dividing a polynomial by a monomial, we divide each term of the polynomial by the monomial.

**2. Applying the Rule**

(5ab - 10b² + 15bc) ÷ 5b = (5ab ÷ 5b) - (10b² ÷ 5b) + (15bc ÷ 5b)

**3. Simplifying Each Term**

**(5ab ÷ 5b)**= a (5 and 5 cancel out, b and b cancel out leaving only a)**(10b² ÷ 5b)**= 2b (10 divided by 5 is 2, b² divided by b is b)**(15bc ÷ 5b)**= 3c (15 divided by 5 is 3, b and b cancel out leaving only c)

**4. Combining the Simplified Terms**

Therefore, the simplified expression is: **a - 2b + 3c**

**Final Answer:** (5ab - 10b² + 15bc) ÷ 5b = **a - 2b + 3c**