[tex]f(x) = x^2 - 4x + 3\\\frac{f(x + h) - f(x)}{h} = \frac{(x + h)^2 - 4(x +h) + 3 - (x^2 - 4x + 3)}{h} = \frac{x^2 + 2xh + h^2 - 4x - 4h + 3 - x^2 + 4x - 3}{h}\\= \frac{2xh + h^2 - 4h}{h} = \frac{h(2x + h - 4)}{h} = 2x + h - 4[/tex]
