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(3x^2+9x+7)/(x+1)-(2x^2+4x-3)/(x-1)-(x^3+x+1)/(x^2-1)这个题.难道到了[(3x^2+9x+7)(x-1)-(2x^2+4x-3)(x+1)-(x^3+x+1)]/(x^2-1)这一步就直接出了答案-(4x+5)/(x^2-1)了吗?
题目详情
(3x^2+9x+7)/(x+1)-(2x^2+4x-3)/(x-1)-(x^3+x+1)/(x^2-1)这个题.
难道到了[(3x^2+9x+7)(x-1)-(2x^2+4x-3)(x+1)-(x^3+x+1)]/(x^2-1)这一步就直接出了答案-(4x+5)/(x^2-1)了吗?
难道到了[(3x^2+9x+7)(x-1)-(2x^2+4x-3)(x+1)-(x^3+x+1)]/(x^2-1)这一步就直接出了答案-(4x+5)/(x^2-1)了吗?
▼优质解答
答案和解析
(3x²+9x+7)/(x+1)-(2x²+4x-3)/(x-1)-(x^3+x+1)/(x²-1)
=(3x²+9x+7)/(x+1)-(2x²+4x-3)/(x-1)-(x^3+x+1)/[(x+1)(x-1)]
=[(3x²+9x+7)(x-1)-(2x²+4x-3)(x+1)-(x^3+x+1)]/[(x+1)(x-1)]
=[3x^3+9x²+7x-3x²-9x-7-2x^3-4x²+3x-2x²-4x+3-x^3-x-1]/[(x+1)(x-1)]
=(5x-5)/[(x+1)(x-1)]
=5/(x+1)
=(3x²+9x+7)/(x+1)-(2x²+4x-3)/(x-1)-(x^3+x+1)/[(x+1)(x-1)]
=[(3x²+9x+7)(x-1)-(2x²+4x-3)(x+1)-(x^3+x+1)]/[(x+1)(x-1)]
=[3x^3+9x²+7x-3x²-9x-7-2x^3-4x²+3x-2x²-4x+3-x^3-x-1]/[(x+1)(x-1)]
=(5x-5)/[(x+1)(x-1)]
=5/(x+1)
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