Rút gọn biểu thức và tìm đkxđ

`M=((x-2)/(2x-2)+3/(2x-2)-(x+3)/(2x+2)):(1-(x-3)/(x+1))` với `x\ne+-1`

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

`= [(x+1)/(2x-2) - (x+3)/(2x+2)]: 4/(x+1) `

`= [(x+1)/[2(x-1)] - (x+3)/[2(x+1)]] : 4/(x+1) `

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

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

`= 4/[2(x-1)(x+1)] : 4/(x+1)`

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

`= 2/[4(x-1)] `

`= 1/[2(x-1)]`