Toán Lớp 8: (x^2+2/x^3-1+x/x^2+x+1+1/1-x) : x-1/2

Question

Toán Lớp 8:  (x^2+2/x^3-1+x/x^2+x+1+1/1-x) : x-1/2

doanthulan · Answer

Giải đáp + Lời giải và giải thích chi tiết:    ((x&sup2;+2)/(x&sup3;-1)+x/(x&sup2;+x+1) +1/(1-x)): (x-1)/2        (x ne1)   = ((x&sup2;+2)/((x-1)(x&sup3;+x+1))+x/(x&sup2;+x+1) - 1/(x-1)) : (x-1)/2   = ( (x&sup2;+2)/((x-1)(x&sup3;+x+1)) + (x(x-1))/((x-1)(x&sup2;+x+1))-(x&sup2;+x+1)/((x-1)(x&sup2;+x+1))) : (x-1)/2   = (x&sup2;+2+x&sup2;-x-x&sup2;-x-1)/((x-1)(x&sup2;+x+1)) . 2/(x-1)   = (x&sup2;-2x+1)/((x-1)(x&sup2;+x+1)). 2/(x-1)   = ((x-1)&sup2;)/((x-1)(x&sup2;+x+1)) . 2/(x-1)   = (x-1)/(x&sup2;+x+1) . 2/(x-1)   = 2/(x&sup2;+x+1)

maitrucloan · Answer

Giải đáp:     ([x^2+2]/[x^3-1]+x/[x^2+x+1]+1/[1-x]) : [x-1]/2    = ({x^2 + 2}/{(x - 1).(x^2 + x + 1)} + {x.(x - 1)}/{(x - 1).(x^2 + x + 1)} - {x^2 + x + 1}/{(x - 1).(x^2 + x + 1)}) : [x-1]/2    = ({x^2 + 2}/{(x - 1).(x^2 + x + 1)} + {x^2 - x}/{(x - 1).(x^2 + x + 1)} - {x^2 + x + 1}/{(x - 1).(x^2 + x + 1)}) : [x-1]/2    = ({x^2 +2 + x^2 - x - x^2 - x - 1}/{(x - 1).(x^2 + x + 1)}) : [x-1]/2    = {x^2 - 2x + 1}/{(x - 1).(x^2 + x + 1)} : [x-1]/2    = {(x - 1)^2}/{(x - 1).(x^2 + x + 1)} : [x-1]/2    = {x - 1}/{x^2 + x + 1} : [x-1]/2    = {x - 1}/{x^2 + x + 1} . 2/{x - 1}   = 2/{x^2 + x + 1}    ∘ dariana