通分:2x/x²-9 x+2/x²+5x+6

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通分:2x/x²-9 x+2/x²+5x+6

x²-9=(x+3)(x-3)
x²+5x+6=(x+2)(x+3)
最简公分母是(x+2)(x+3)(x-3)
所以2x/(x²-9)=2x(x+2)/(x+2)(x+3)(x-3)
(x+2)/(x²+5x+6)=(x+2)(x-3)/(x+2)(x+3)(x-3)

2x/x²-9

x+2/x²+5x+6=(x+2)/(x+2)(x+3)=1/(x+3)=(x-3)/(x²-9)

2x/(x²-9)=2x/(x-3)*(x+3)
(x+2)/(x²+5x+6)=(x+2)/(x+2)*(x+3)=1/(x+3)=(x-3)/(x-3)*(x+3)