(x+2/2x^2-3x-x^2+2x/2x^2+x-6)/（1/2-1/4x-6）
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解决时间 2021-02-07 17:24
- 提问者网友：最美的风景
- 2021-02-06 17:23
(x+2/2x^2-3x-x^2+2x/2x^2+x-6)/（1/2-1/4x-6）
最佳答案
- 五星知识达人网友：零点过十分
- 2021-02-06 17:30
{ (x+2)/(2x^2-3x) - (x^2+2x)/(2x^2+x-6) } / {1/2-1/(4x-6) }
= { (x+2)/[x(2x-3)] - x(x+2)/[(x+2)(2x-3)]} / {1/2-1/[2(2x-3)] }
= { (x+2)/[x(2x-3)] - x/(2x-3) } / {1/2-1/[2(2x-3)] }
分子分母同乘以2x(2x-3)：
= {2(x+2) - 2x^2} / {x(2x-3)-x }
= {2x+4- 2x^2} / {2x^2-3x-x }
=- {2x^2-2x+4} / {2x^2-4x }
=- 2(x+1)(x-2) / {2x(x-2) }
= - (x+1) / x
= { (x+2)/[x(2x-3)] - x(x+2)/[(x+2)(2x-3)]} / {1/2-1/[2(2x-3)] }
= { (x+2)/[x(2x-3)] - x/(2x-3) } / {1/2-1/[2(2x-3)] }
分子分母同乘以2x(2x-3)：
= {2(x+2) - 2x^2} / {x(2x-3)-x }
= {2x+4- 2x^2} / {2x^2-3x-x }
=- {2x^2-2x+4} / {2x^2-4x }
=- 2(x+1)(x-2) / {2x(x-2) }
= - (x+1) / x
全部回答
- 1楼网友：末日狂欢
- 2021-02-06 17:54
（x+2/2x²-3x 减去 x²+2x/2x²+x-6）除以 （1/2 减去 1/4x-6)
= [(x+2) / x(2x-3) - x(x+2) / (2x-3)(x+2) ] / [1/2 - 1/(4x-6)]
= [(x+2) / x(2x-3) - x / (2x-3)] / [1/2 - 1/(4x-6)]
= [(x+2-x²) / x(2x-3)] / [1/2 - 1/(4x-6)]
= -[(x-2)(x+1) / x(2x-3)] / [1/2 - 1/(4x-6)]
= -[(x-2)(x+1) / x(2x-3)] / {1/2 * [1 - 1/(2x-3)]}
= -[(x-2)(x+1) / x(2x-3)] / {1/2 * [(2x-4)/(2x-3)]}
= -[(x-2)(x+1) / x(2x-3)] / [(x-2)/(2x-3)]
= -[(x-2)(x+1) / x(2x-3)] * [(2x-3) / (x-2)]
= -[(x-2)(x+1)(2x-3)] / [x(2x-3)(x-2)]
= - (x+1)/x
= -1 - 1/x
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