Rút Gọn : `A=(x-(x^2+2)/(x+1)):(x/(x+1)-(x-4)/(1-x^2))` 11/08/2021 Bởi Athena Rút Gọn : `A=(x-(x^2+2)/(x+1)):(x/(x+1)-(x-4)/(1-x^2))`
`A=(x-(x^2+2)/(x+1)):(x/(x+1)-(x-4)/(1-x^2)) (ĐKXĐ : x\ne +-1)` ` =((x.(x+1))/(x+1) – (x^2+2)/(x+1)):(x/(x+1) – (x-4)/((1-x).(x+1)))` ` = ((x^2+x)/(x+1) – (x^2+2)/(x+1)) : ((x.(1-x))/((x+1).(1-x)) – (x-4)/((1-x).(x+1)))` ` = (x^2 + x – x^2-2)/(x+1) : (x.(1-x) – x + 4)/((x+1).(1-x))` ` = (x-2)/(x+1) : (x – x^2 – x +4)/((x+1).(1-x))` ` = (x-2)/(x+1) : (4-x^2)/((x+1).(1-x))` ` = (x-2)/(x+1) : (x^2 – 4)/((x-1).(x+1))` ` = (x-2)/(x+1) : ((x-2).(x+2))/((x-1).(x+1))` ` = (x-2)/(x+1) . ((x-1).(x+1))/((x-2).(x+2))` ` = (x-1)/(x+2)` Vậy `A = (x-1)/(x+2)` với `x\ne +-1` Bình luận
Đáp án:
Giải thích các bước giải:
`A=(x-(x^2+2)/(x+1)):(x/(x+1)-(x-4)/(1-x^2)) (ĐKXĐ : x\ne +-1)`
` =((x.(x+1))/(x+1) – (x^2+2)/(x+1)):(x/(x+1) – (x-4)/((1-x).(x+1)))`
` = ((x^2+x)/(x+1) – (x^2+2)/(x+1)) : ((x.(1-x))/((x+1).(1-x)) – (x-4)/((1-x).(x+1)))`
` = (x^2 + x – x^2-2)/(x+1) : (x.(1-x) – x + 4)/((x+1).(1-x))`
` = (x-2)/(x+1) : (x – x^2 – x +4)/((x+1).(1-x))`
` = (x-2)/(x+1) : (4-x^2)/((x+1).(1-x))`
` = (x-2)/(x+1) : (x^2 – 4)/((x-1).(x+1))`
` = (x-2)/(x+1) : ((x-2).(x+2))/((x-1).(x+1))`
` = (x-2)/(x+1) . ((x-1).(x+1))/((x-2).(x+2))`
` = (x-1)/(x+2)`
Vậy `A = (x-1)/(x+2)` với `x\ne +-1`