(1) 化简：2/(x+1)(x+3)+2/(x+3)(x+5)+2/(x+5)(x+7)+...+2/(x+2009)

来源：学生作业帮编辑：搜搜做题作业网作业帮分类：数学作业时间：2024/05/15 01:26:39

(1) 化简：2/(x+1)(x+3)+2/(x+3)(x+5)+2/(x+5)(x+7)+...+2/(x+2009)(x+2011)
(2) 若对于一切不为0且不为-2的实数x,(5x+4)/x(x+2)=A/x+B(x+2),求常数A,B的值

2/(x+1)(x+3)+2/(x+3)(x+5)+2/(x+5)(x+7)+...+2/(x+2009)(x+2011)
=1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+1/(x+5)-1/(x+7)+...+1/(x+2009)-1/(x+2011)
=1/(x+1)-1/(x+2011)
=(x+2011)/(x+1)(x+2011)-(x+1)/(x+1)(x+2011)
=(x+2011-x-1)/(x+1)(x+2011)
=2010/(x+1)(x+2011)
(5x+4)/x(x+2)=A/x+B/(x+2)
(5x+4)/x(x+2)=A(x+2)/x(x+2)+Bx/x(x+2)
(5x+4)/x(x+2)=[A(x+2)+Bx]/x(x+2)
(5x+4)/x(x+2)=[Ax+2A+Bx]/x(x+2)
(5x+4)/x(x+2)=[(A+B)x+2A]/x(x+2)
A+B=5
2A=4
解得
A=2
B=3

|X-1|+|X-2|+|X-3|+|X-4|+|X-5|+|X-6|+|X-7|+|X-8|+|X-9|+|X-10| x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4 x^5+x^4 = (x^3-x)(x^2+x+1)+x^2+x 解方程x/(x-2)=2x/(x-3)+(1-x)/(x-5x+6) (2x-1)/(x-1)(x-2)=(x-5)/(x-2)(x-3) x/2x^2-11x-21=(x+7)/x^2-1 已知1+x+x^2+x^3=0,求x+x^2+x^3+x^4+x^5+x^6+x^7+x^8的值 y=(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(x-10)的导数在x=1 设函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(x-10), (3-x)/(1-x)-(5-x)/(7-x)+(x^2-x)/(x^2-8x+7)=1 解方程(x+1/x+2)-(x+2/x+3)=(x+5/x+6)-(x+6/x+7) 解方程：x+2/x+1-x+3/x+2=x+6/x+5-x+7/x+6 x-1\x-2+x-6\x-7=x-2\x-3+x-5\x-6 分式方程