1. **State the problem:** A school has $5x + 10$ books shared equally among $x$ students. We need to write the rational expression for books per student and then simplify it. 2. **Write the rational expression:** The number of books per student is the total books divided by the number of students: $$\frac{5x + 10}{x}$$ 3. **Simplify the expression:** Factor the numerator: $$\frac{\cancel{x}(5 + \frac{10}{x})}{\cancel{x}} = \frac{5(x + 2)}{x}$$ More explicitly, factor out 5: $$\frac{5(x + 2)}{x}$$ Since $x$ is in the denominator and cannot be canceled with anything in the numerator, the simplified form is: $$\frac{5(x + 2)}{x}$$ 4. **Explain:** The expression means each student gets $\frac{5(x + 2)}{x}$ books. We factored the numerator to see the structure clearly but cannot cancel $x$ because it is only in the denominator. **Final answer:** $$\frac{5(x + 2)}{x}$$