Question

Спростіть вираз (2х - 1 1 9х+6)
( ----------- +-------+-----------)
( Х^2+2х+4 х-2 х^3-8)
х^2-4
×------------
9

Answer 1

((2x-1)/(x^2+2x+4)+1/(x-2)+(9x+6)/(x^3-8))*(x^2-4)/9=(((2x-1)(x-2)+(x^2+2x+4)+(9x+6))/(x^3-8))*(x^2-4)/9=((2x^2-4x-x+2+x^2+2x+4+9x+6)/(x^3-8))*(x^2-4)/9=(3x^2+6x+12)/(x^3-8)*(x^2-4)/9
=(3(x^2+2x+4))/((x-2)(x^2+2x+4))*((x-2)(x+2))/9=(x+2)/3