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分式化简(要求解答过程)(1)1/(x+1)+1/(x+3)-1/(x+5)-1/(x+7)(2)[(x^2+x-2)/(x^2+7x+12)]÷[(x^2+x-2)/(x^2-x-12)]÷[(x^2+3x-4)/(x^2-6x+8)]
题目详情
分式化简(要求解答过程)
(1) 1/(x+1)+1/(x+3)-1/(x+5)-1/(x+7)
(2) [(x^2+x-2)/(x^2+7x+12)]÷[(x^2+x-2)/(x^2-x-12)]÷[(x^2+3x-4)/(x^2-6x+8)]
(1) 1/(x+1)+1/(x+3)-1/(x+5)-1/(x+7)
(2) [(x^2+x-2)/(x^2+7x+12)]÷[(x^2+x-2)/(x^2-x-12)]÷[(x^2+3x-4)/(x^2-6x+8)]
▼优质解答
答案和解析
(1)
原式=4/(x+1)(x+5)-4/(x+3)(x+7)
=4(5x+16)/(x+1)(x+3)(x+5)(x+7)
(2)
分子：(x^2+x-2)*(x-4)(x+3)*(x-2)(x-4)
分母：(x+3)(x+4)*(x^2+x-2)*(x+4)(x-1)
约分得到 [(x-4)^2(x-2)]/[(x+4)^2(x-1)]
原式=4/(x+1)(x+5)-4/(x+3)(x+7)
=4(5x+16)/(x+1)(x+3)(x+5)(x+7)
(2)
分子：(x^2+x-2)*(x-4)(x+3)*(x-2)(x-4)
分母：(x+3)(x+4)*(x^2+x-2)*(x+4)(x-1)
约分得到 [(x-4)^2(x-2)]/[(x+4)^2(x-1)]
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