`(x+2)/(x-1) . (x^3/(2x+2) +1) – (8x+7)/(2x^2-2)`

0 bình luận về “`(x+2)/(x-1) . (x^3/(2x+2) +1) – (8x+7)/(2x^2-2)`”

1. Đáp án:

   `(x²+2x+3)/2`

   Giải thích các bước giải:

   `(x+2)/(x-1).((x³)/(2x+2)+1)-(8x+7)/(2x²-2)(ĐKXĐ:“x`$\neq$`±1)`

   `=(x+2)/(x-1).[(x³)/[2(x+1)]+[2(x+1)]/[2(x+1)]]-(8x+7)/[2(x²-1)]`

   `=(x+2)/(x-1).(x³+2x+2)/[2(x+1)]-(8x+7)/[2(x²-1)]`

   `=[(x+2)(x³+2x+2)]/[2(x-1)(x+1)]-(8x+7)/[2(x-1)(x+1)]`

   `=(x^4+2x²+2x+2x³+4x+4)/[2(x-1)(x+1)]-(8x+7)/[2(x-1)(x+1)]`

   `=(x^4+2x²+2x+2x³+4x+4-8x-7)/[2(x-1)(x+1)]`

   `=(x^4+2x³+2x²-2x-3)/[2(x-1)(x+1)]`

   `=(x^4+2x³+3x²-x²-2x-3)/[2(x-1)(x+1)]`

   `=(x^4-x²+2x³-2x+3x²-3)/[2(x-1)(x+1)]`

   `=(x²(x²-1)+2x(x²-1)+3(x²-1))/[2(x-1)(x+1)]`

   `=[(x²-1)(x²+2x+3)]/[2(x²-1)]`

   `=(x²+2x+3)/2`

   Bình luận

2. Đáp án:

    `(x^2+2x+3)/2`

   Giải thích các bước giải:

   Với `x\ne+-1`

    `(x+2)/(x-1).(x^3/(2x+2)+1)-(8x+7)/(2x^2-2)`

   `=(x+2)/(x-1).(x^3+2x+2)/(2x+2)-(8x+7)/(2x^2-2)`

   `=((x+2).(x^3+2x+2))/((x-1)(2x+2))-(8x+7)/(2x^2-2)`

   `=((x+2).(x^3+2x+2))/(2(x-1)(x+1))-(8x+7)/(2x^2-2)`

   `=((x+2).(x^3+2x+2))/(2(x-1)(x+1))-(8x+7)/(2(x^2-1))`

   `=((x+2).(x^3+2x+2))/(2(x-1)(x+1))-(8x+7)/(2(x-1)(x+1))`

   `=((x+2).(x^3+2x+2)-(8x+7))/(2(x-1)(x+1))`

   `=(x^4+2x^2+2x+2x^3+4x+4-(8x+7))/(2(x-1)(x+1))`

   `=(x^4+2x^3+2x^2+6x+4-8x-7)/(2(x-1)(x+1))`

   `=(x^4+2x^3+2x^2-2x-3)/(2(x-1)(x+1))`

   `=(x^4-x^2+2x^3-2x+3x^2-3)/(2(x-1)(x+1))`

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

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

   `=(x^2+2x+3)/2`

   Bình luận