Đáp án+Giải thích các bước giải:
`d)P=((x+3)/(x^2-1)-3/(x+1)):(1-2/(x-1))(x ne +-1,x ne 3)`
`P=((x+3)/((x-1)(x+1))-(3(x-1))/((x-1)(x+1))):((x-1-2)/(x-1))`
`P=(x+3-3x+3)/((x-1)(x+1)):(x-3)/(x-1)`
`P=(6-2x)/((x-1)(x+1))*(x-1)/(x-3)`
`P=-2/(x+1)`
`e)P<0`
`<=>-2/(x+1)<0`
Mà `-2<0`
`<=>x+1<0`
`<=>x<-1`
`f)Q=x.P in ZZ`
`Q=(-2x)/(x+1)`
`Q\in ZZ`
`=>2x\vdots x+1`
`=>2x+2-2\vdots x+1`
`=>2\vdots x+1`
`=>x+1\in Ư(2)={+-1,+-2}`
`=>x in {0;-2;1;-3}`
Mà `x\ne 1`
`=>x in {0;-2;-3}`
`4a)M=(1-x/(x+1)):((x+3)/(x-2)+(x+2)/(3-x)+(x+2)/(x^2-5x+6))(x ne 2,x ne 3)`
`M=((x+1-x)/(x+1)):(((x+3)(x-3))/((x-2)(x-3))-((x+2)(x-2))/((x-2)(x-3))+(x+2)/((x-2)(x-3)))`
`M=1/(x+1):((x^2-9-x^2+4+x+2)/((x-2)(x-3)))`
`M=1/(x+1):(x-3)/((x-2)(x-3))`
`M=1/(x+1):1/(x-2)`
`M=(x-2)/(x+1)`
`b)M<0`
`<=>(x-2)/(x+1)<0`
Mà `x-2<x+1`
`<=>{(x+1>0),(x-2<0):}`
`<=>{(x> -1),(x<2):}`
`<=>-1<x<2`
`c)M in ZZ`
`=>x-2\vdots x+1`
`=>x+1-3 vdots x+1`
`=>3 vdots x+1`
`=>x+1 in Ư(3)={+-1,+-3}`
`=>x in {0;-2;2;-4}`
Mà `x ne 2`
`=>x in {0;-2;-4}.`
