Упростите выражение: ( __х3+8____ - __8х3+1__) : (__8х3-1___ + ____х3-8____)     х3-2х2+4х       4х2-2х+1            4х2+2х+1          х3+2х2+4х

  = ((х+2)(х²-2х+4)    -     (2х+1)(4х²-2х+1)  )  ÷ ( (2х-1)(4х²+2х+1) +  (х-2)(х²+2х+4)        х(х²-2х+4)                      (4х²-2х+1)                 (4х²+2х+1)               х(х²+2х+4)     =  х+2   -  х(2х+1)  ×       х                      =   х+2-2х²-х    ×      х                  =   -      (2х²-2)× х                     х                      х(2х-1)+(х-2)             х                     2х²-х+х-2                        х  ×(2х²-2)       =     -  1  

[latex](\frac{x^3+8}{x^3-2x^2+4x}-\frac{8x^3+1}{4x^2-2x+1}):(\frac{8x^3-1}{4x^2+2x+1}+\frac{x^3-8}{x^3+2x^2+4x})=[/latex]   [latex]=(\frac{(x+2)(x^2-2x+4)}{x(x^2-2x+4)}-\frac{(2x+1)(4x^2-2x+1)}{4x^2-2x+1}):(\frac{(2x-1)(4x^2+2x+1)}{4x^2+2x+1}+\\\ \frac{(x-2)(x^2+2x+4)}{x(x^2+2x+4)})=(\frac{x+2}{x}-\frac{2x+1}{1}):(\frac{2x-1}{1}+\frac{x-2}{x})=\\\ \frac{x+2-x(2x+1)}{x}:\frac{x(2x-1)+x-2}{x}=\frac{x+2-2x^2-x}{x}*\frac{x}{2x^2-x+x-2}=\\\ =\frac{2-2x^2}{2x^2-2}=-\frac{2x^2-2}{2x^2-2}=-1 [/latex]