Question

求高手解答一道数学题

（2x/（x²-9））-(1/（3-x）)-(2/（x²+6x+9））
打错了不是-(1/（3-x）)而是+(1/（3-x）)

Answer 1

原式=2x/(x+3)(x-3)+1/(x-3)-2/(x+3)²
=(2x²+6x+x²+6x+9-2x+6)/(x+3)²(x-3)
=(3x²+10x+15)/(x+3)²(x-3)

追问

打错了 是+(1/（3-x）) 不是-(1/（3-x）) 求你帮帮我

追答

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

追问

(x²-2x-3)怎么变成(x-3)(x+2)的

追答

哦，对不起
原式=2x/(x+3)(x-3)-1/(x-3)-2/(x+3)²
=(2x²+6x-x²-6x-9-2x+6)/(x+3)²(x-3)
=(x²-2x-3)/(x+3)²(x-3)
=(x-3)(x+1)/(x+3)²(x-3)
=(x+1)/(x+3)²

追问

我就是不明白(x²-2x-3)怎么变成(x-3)(x+1)的 希望你可以给我详细解答我会选为满意以及提高悬赏

追答

x²-2x-3
=x²-3x+x-3
=x(x-3)+(x-3)
=(x-3)(x+1)

Answer 2

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

Answer 3

原等式=2x/(x+3)(x-3)-1/(x-3)-2/(x+3)^2
=[2x(x+3)-（x+3)^2-2(x-3)]/（x+3)^2(x-3)
=[x^2-2x-3]/(x+3)^2(x-3)