Question

Se da $E(x) = (x+2)(x-2)+3x+6$
$x \neq 1$
$x \neq 2$
  Calculati $F(x) = \frac{E(x+1) - E(x)}{(x+2)(x+1)}$

Answer 1

[tex]F(x)= \frac{[(x+1+2)(x+1-2)+3(x+1)+6]-(x+2)(x-2)+3x+6}{(x+2)(x-1)} \\ F(x)=\frac{[(x+1)^2-2^2)+3x+3+6]-(x^2-2^2)+3x+6}{(x+2)(x-1)} \\ F(x)=\frac{ x^{2} +2x+1-4+3x+9- x^{2} +4+3x+6}{(x+2)(x-1)} \\ F(x)=\frac{8x+16}{(x+2)(x-1)} \\ F(x)=\frac{8(x+2)}{(x+2)(x-1)} \\ F(x)=\frac{8}{x-1} [/tex]