Đáp án:
`A=(x+1)/(x-2)`
Giải thích các bước giải:
`A=(x+1)/(x+3)-10/(x^2+x-6)-5/(2-x)(x\ne2,x\ne-3)`
`=(x+1)/(x+3)-10/(x^2+3x-2x-6)+5/(x-2)`
`=(x+1)/(x+3)-10/[x(x+3)-2(x+3)]+5/(x-2)`
`=(x+1)/(x+3)-10/[(x+3)(x-2)]+5/(x-2)`
`=[(x+1)(x-2)]/[(x+3)(x-2)]-10/[(x+3)(x-2)]+[5(x+3)]/[(x+3)(x-2)]`
`=[(x+1)(x-2)-10+5(x+3)]/[(x+3)(x-2)]`
`=(x^2-2x+x-2-10+5x+15)/[(x+3)(x-2)]`
`=(x^2+4x+3)/[(x+3)(x-2)]`
`=(x^2+3x+x+3)/[(x+3)(x-2)]`
`=[x(x+3)+(x+3)]/[(x+3)(x-2)]`
`=[(x+3)(x+1)]/[(x+3)(x-2)]`
`=(x+1)/(x-2)`
