Rút gọn bt `3) {1}/{x^2 – x + 1} + 1 – {x^2 + 2}/{x^3 + 1}`

2 bình luận về “Rút gọn bt `3) {1}/{x^2 – x + 1} + 1 – {x^2 + 2}/{x^3 + 1}`”

1. $$ 3)1/(x^2-x+1)+1-(x^2+2)/(x^3+1) (x≠-1)

   $$ =(x+1)/((x+1)(x^2-x+1))+((x+1)(x^2-x+1))/((x+1)(x^2-x+1))-(x^2+2)/((x+1)(x^2-x+1))

   $$ =(x+1+x^3+1-x^2-2)/((x+1)(x^2-x+1))

   $$ =(x^3-x^2+x)/((x+1)(x^2-x+1))

   $$ =(x.(x^2-x+1))/((x+1)(x^2-x+1))

   $$ =x/(x+1)

   Trả lời
2. 3, 1/(x^2 – x + 1) + 1 – (x^2 + 2)/(x^3 + 1)    (ĐK: x \ne -1)

   = (x + 1)/((x + 1)(x^2 – x + 1)) + ((x + 1)(x^2 – x + 1))/((x + 1)(x^2 – x + 1)) – (x^2 + 2)/((x + 1)(x^2 – x + 1)

   = (x + 1 + x^3 +1 – x^2 – 2)/((x + 1)(x^2 – x + 1)

   = (x^3 – x^2 + x )/((x + 1)(x^2 – x + 1)

   = (x(x^2 – x + 1))/((x + 1)(x^2 – x + 1))

   = x/(x + 1)

   $\text{You can't use 'macro parameter character \#' in math mode}$

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