Chapter 3.4, Problem 26P

Suppose you start with a fraction and you add 1 to both the numerator and the denominator. For example, if you started with $\frac{2}{3},$ then you’d get a new fraction $\frac{2+1}{3+1}=\frac{3}{4}.$ Is this procedure of adding 1 to the numerator and the denominator the same as adding the number 1 to the original fraction? (For example, is $\frac{2+1}{3+1}$ equal to $\frac{2}{3}+1?)$ Explain your answer.