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

tanhuyngo1234

2 năm trước

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thuyhangdinh7851

Đáp án `:`

`1/{1-x}`

Lời giải chi tiết `:`

Điều kiện xác định `:` `1-x``ne``0``->``x``ne``1`

`x^4/{1-x}+x^3+x^2+x+1`

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

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

`=` `{x^4+x^3-x^4+x^2-x^3+x-x^2+1-x}/{1-x}`

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

`=` `1/{1-x}`

Vậy `:` `x^4/{1-x}+x^3+x^2+x+1=1/{1-x}`

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neo_2580

Đáp án:

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

Giải thích các bước giải:

`ĐKXĐ:x\ne1`

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

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

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

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

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

`=1/(1-x)`

Vậy `x^4/(1-x)+x^3+x^2+x+1=1/(1-x)`

Vote (0) Phản hồi (0) 2 năm trước

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