Question

Simplifique a expressão abaixo

Answer 1

$(x+1)^2=x^2+2x+1\\ (x-1)^2=x^2-2x+1\\ (x+1)\cdot(x-1)=x^2-1\\ 3\cdot(-2x+3)=-6x+9\\ \\----------------------\\ \\ \ \ \frac{(x+1)^2-2x^2+(x-1)^2+(x+1)\cdot(x-1)+3\cdot(-2x+3)-1}{(x-3)\cdot(x+3)}\\ \\= \frac{x^2+2x+1-2x^2+x^2-2x+1+x^2-1-6x+9-1}{(x-3)\cdot(x+3)}\\ \\= \frac{x^2-2x^2+x^2+x^2+2x-2x-6x+1+1-1+9-1}{(x-3)\cdot(x+3)}\\ \\= \frac{x^2-6x+9}{(x-3)\cdot(x+3)}\\ \\= \frac{(x-3)\cdot(x-3)}{(x-3)\cdot(x+3)}\\ \\= \frac{x-3}{x+3}$

Resposta: C