(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
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/17 11:34:09
![(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](/uploads/image/z/5623501-13-1.jpg?t=%281%29+%E5%8C%96%E7%AE%80%EF%BC%9A2%2F%28x%2B1%29%28x%2B3%29%2B2%2F%28x%2B3%29%28x%2B5%29%2B2%2F%28x%2B5%29%28x%2B7%29%2B...%2B2%2F%28x%2B2009%29%28x%2B2011%29%282%29+%E8%8B%A5%E5%AF%B9%E4%BA%8E%E4%B8%80%E5%88%87%E4%B8%8D%E4%B8%BA0%E4%B8%94%E4%B8%8D%E4%B8%BA-2%E7%9A%84%E5%AE%9E%E6%95%B0x%2C%285x%2B4%29%2Fx%28x%2B2%29%3DA%2Fx%2BB%28x%2B2%29%2C%E6%B1%82%E5%B8%B8%E6%95%B0A%2CB%E7%9A%84%E5%80%BC)
(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
(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
(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
(1)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+2009)-1/(x+2011)=1/(x+1)-1/(x+2011)=2010/(x+1)(x+2011)
(2)(5x+4)/x(x+2)=A/x+B/(x+2),A/x+B/(x+2)=[A(x+2)+Bx]/X(X+2),因此A+B=5,2A=4,随意A=2,B=3