Đáp án:
`a)(5a²-3a+1)/(a³+1)`
`b)(6a+1)/(a²-4)`
Giải thích các bước giải:
`a)3/(a+1)+(2a-2)/(a²-a+1)(ĐKXĐ:``a`$\neq$ `-1)`
`=[3(a²-a+1)]/[(a+1)(a²-a+1)]+[(2a-2)(a+1)]/[(a+1)(a²-a+1)]`
`=[3(a²-a+1)+(2a-2)(a+1)]/[(a+1)(a²-a+1)]`
`=(3a²-3a+3+2a²+2a-2a-2)/[(a+1)(a²-a+1)]`
`=[(3a²+2a²)+(-3a+2a-2a)+(3-2)]/[(a+1)(a²-a+1)]`
`=(5a²-3a+1)/(a³+1)`
`b)2/(a+2)+(a-1)/(a²-4)+3/(a-2)(ĐKXĐ:``a`$\neq$ `±2)`
`=[2(a-2)]/[(a+2)(a-2)]+(a-1)/[(a+2)(a-2)]+[3(a+2)]/[(a+2)(a-2)]`
`=[2(a-2)+a-1+3(a+2)]/[(a+2)(a-2)]`
`=(2a-4+a-1+3a+6)/[(a+2)(a-2)]`
`=[(2a+a+3a)+(-4-1+6)]/[(a+2)(a-2)]`
`=(6a+1)/(a²-4)`
