Question

(2*x^3 + 6*x^2 - 8*x + 3)/(x^2 + 2*x - 3) выразите целую часть

Answer 1

$\frac{2x^3+6x^2-8x+3}{x^2+2x-3} = \frac{2(x^3+2x^2-3x-2x^2+3x)+6x^2-8x+3}{x^2+2x-3} =$
$= \frac{2(x^3+2x^2-3x)-4x^2+6x+6x^2-8x+3}{x^2+2x-3} =$
$=\frac{2x(x^2+2x-3)+2x^2-2x+3}{x^2+2x-3}=2x+ \frac{2(x^2+2x-3-2x+3)-2x+3}{x^2+2x-3} =$
$=2x+ \frac{2(x^2+2x-3-2x+3)-2x+3}{x^2+2x-3} = 2x+ \frac{2(x^2+2x-3)-4x+6-2x+3}{x^2+2x-3}=$
$=2x+2 +\frac{-6x+9}{x^2+2x-3}$

Целая часть: 2x + 2