Question

E(x)= x^2-9 supra x^2-4x+3 + x+2 supra x+1 -x^2+5x+2 supra x^2-1

Answer 1

$E_{(x)} = \frac{x^2-9}{x^2+4x+3} + \frac{x+2}{x+1} - \frac{x^2+5x+2}{x^2-1} \\ = \frac{(x+3)(x-3)}{ (x+1)(x+3)} + \frac{x+2}{x+1} - \frac{x^2+5x+2}{(x+1)(x-1)} = \frac{(x-3)(x-1)+(x+2)(x-1)-(x^2+5x+2) }{(x+1)(x-1)} \\ = \frac{x^2-x-3x+3+x^2-x+2x-2-x^2-5x-2}{(x+1)(x-1)} = \frac{x^2-8x-1}{(x+1)(x-1)}$