Cho phân thức : P = ($\frac{x+1}{x-1}$+$\frac{1-3x}{x^{3}+x}$):$\frac{x-1}{x^{2}+1}$ b)Rút gọn P

Đáp án:

`P = ([x+1]/[x−1]+[1−3x]/[x^3+x]):[x−1]/[x^2+1]` 

`P = ([x+1]/[x−1]+[1−3x]/[x.(x^2 + 1)]):[x−1]/[x^2+1]`

`P = ([(x +1).x.(x^2 + 1)]/[(x -1).x.(x^2 + 1)]+[(1−3x).(x - 1)]/[(x -1).x.(x^2 + 1)]):[x−1]/[x^2+1]`

`P = ([x^4 + x^3 + x^2 + x]/[(x -1).x.(x^2 + 1)]+[-3x^2  + 4x - 1]/[(x -1).x.(x^2 + 1)]):[x−1]/[x^2+1]`

`P = [x^4 + x^3 + x^2 + x -3x^2  + 4x - 1]/[(x -1).x.(x^2 + 1)] . [x^2 + 1]/[x - 1]`

`P = [x^4 + x^3 -2x^2 + 5x - 1]/[(x -1).x.(x^2 + 1)] . [x^2 + 1]/[x - 1]`

`P = [x^4 + x^3 -2x^2 + 5x - 1]/[x.(x - 1)^2]`

`#dariana`