Question

]3x/x+2 + x+4/x²-4 - x+1/x-2[/tex]

Answer 1

Resposta:

$Por-divisao- de- polinomio:\\\\x^2-4x+1 :(x-2)= Quociente-> -x+2\\ -x^2+2x \\ -2x+1\\+2x-4\\Resto -> -3$

Explicação passo-a-passo:

$\frac{3x}{x+2} +x+\frac{4}{x^2-4} -\frac{x+1}{x-2} \\\\mmc: x^2-2^2= (x+2)(x-2)\\\\\frac{3x}{(x+2)(x-2)} +x+\frac{4}{(x+2)(x-2)} - \frac{x+1}{(x+2)(x-2)} \\\frac{3x(x-2)}{(x+2)(x-2)} +\frac{x(x+2)(x-2)}{(x+2)(x-2)} +\frac{4}{(x+2)(x-2)} -\frac{x+1(x+2)}{(x+2)(x-2)}\\\frac{(3x^2-6x)+(x^2+2x)(x-2)+(4)-(x^2+2x+x+2)}{(x+2)(x-2)} \\\frac{3x^2+6x+x^3 -2x^2+2x^2-4+4-x^2+3x+2}{(x+2)(x-2)} \\\frac{x^3+3x^2-2x^2+2x^2-x^2+6x+3x-4+4+2}{(x+2)(x-2)} \\\frac{x^3+2x^2+9x+2}{(x+2)(x-2)}$

$\\\frac{(x^2-4x+1)(x+2))}{(x+2)(x-2)} \\\frac{x^2-4x+1}{(x-2)}$

A continuação está na resposta.