Why is $\frac{1}{2}\frac{b^{2}-a^{2}}{b-a} = \frac{a+b}{2}$?

Question

Why is $$\frac{1}{2}\frac{b^{2}-a^{2}}{b-a} = \frac{a+b}{2}$$?

Answer 1

Consider that $b^2-a^2 = (b+a)(b-a)$

Answer 2

$$\frac{1}{2}\frac{b^{2}-a^{2}}{b-a}$$ =$$\frac{1}{2}\frac{(b+a)(b-a)}{b-a} =\frac{a+b}{2}$$