Question

把分式：x/(x+1)(x+2),2/x^2+2x+1,-1/3x+6,通分后相加,分子为什么?

Answer 1

x/(x+1)(x+2),2/x²+2x+1,-1/3x+6,通分后相加,

原式＝x/【(x+1)(x+2)】+2/(x+1)²-1/3(x+2)

=3x(x+1)/【3(x+1)²(x+2)】+6(x+2)/[3(x+1)²(x+2)]-(x+1)²/[3(x+1)²(x+2)]

=[3x²+3x+6x+12-x²-2x-1]/[3(x+1)²(x+2)

=[2x²+7x+11]/[3(x+1)²(x+2)].

已是最简,三式相加,分子是：2x²+7x+11 ,