`a)`
Ta có:
`(x-3)(x+1).3(x+3)=3(x+3)(x-3)(x+1)`
`(3x+3).(x^2-9)=3(x+3)(x-3)(x+1)`
`⇒(x-3)(x+1).3(x+3)=(3x+3).(x^2-9)`
`⇒[(x-3)(x+1)]/(3x+3)=(x^2-9)/[3(x+3)]`
`⇒đpcm`
`b)`
Ta có:
`(x^3-x^2).(x-1)=x^2(x-1)(x-1)=x^2(x-1)^2`
`(x^3-2x^2+x).x=x.(x^2-2x+1).x=x^2(x-1)^2`
`⇒(x^3-x^2).(x-1)=(x^3-2x^2+x).x`
`⇒(x^3-x^2)/(x^3-2x^2+x)=x/(x-1)`
`⇒đpcm`
`c)`
Ta có:
`(x^2-7x+10).(x-1)`
`=(x^2-2x-5x+10).(x-1)`
`=[x(x-2)-5(x-2)].(x-1)`
`=(x-1)(x-2)(x-5)`
`(x^2-6x+5).(x-2)`
`=(x^2-5x-x+5).(x-2)`
`=[x(x-5)-(x-5)].(x-2)`
`=(x-1)(x-2)(x-5)`
`⇒(x^2-7x+10).(x-1)=(x^2-6x+5).(x-2)`
`⇒(x^2-7x+10)/(x^2-6x+5)=(x-2)/(x-1)`
`⇒đpcm`
`d)`
Ta có:
`(x^2-2xy+y^2).(x+2y)=(x-y)^2(x+2y)`
`(x^2+xy-2y^2).(x-y)`
`=(x^2-xy+2xy-2y^2).(x-y)`
`=[x(x-y)+2y(x-y)].(x-y)`
`=(x-y)(x+2y)(x-y)`
`=(x-y)^2(x+2y)`
`⇒(x^2-2xy+y^2).(x+2y)=(x^2+xy-2y^2).(x-y)`
`⇒(x^2-2xy+y^2)/(x^2+xy-2y^2)=(x-y)/(x+2y)`
`⇒đpcm`
