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

Question

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

score 4 · Accepted Answer · answered Nov 27 '17 at 16:12

4

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

answered Nov 27 '17 at 16:12

RJM

1

Ah now i see, i thought $b^2-a^2 = (b-a)^{2} = (b-a)(b-a)$ which is wrong. – M.Mac Nov 27 '17 at 16:14

score 0 · Answer 2 · answered Nov 27 '17 at 16:31

0

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

answered Nov 27 '17 at 16:31

Atharva Shetty

2 Answers2