3x+5/(x+2)(x+3)=A/(x+2)+B/x+3,求(3A+B)的2008次方
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3x+5/(x+2)(x+3)=A/(x+2)+B/x+3,求(3A+B)的2008次方3x+5/(x+2)(x+3)=A/(x+2)+B/x+3,求(3A+B)的2008次方3x+5/(x+2)(x
3x+5/(x+2)(x+3)=A/(x+2)+B/x+3,求(3A+B)的2008次方
3x+5/(x+2)(x+3)=A/(x+2)+B/x+3,求(3A+B)的2008次方
3x+5/(x+2)(x+3)=A/(x+2)+B/x+3,求(3A+B)的2008次方
3x+5/(x+2)(x+3)=A/(x+2)+B/x+3
两边同乘以(x+2)(x+3)得:
3x+5=A(x+3)+B(x+2)
3x+5=(A+B)x+3A+2B
所以:
A+B=3
3A+2B=5
解得:A=-1;B=4
(3A+B)的2008次方=1的2008次方=1
将等式右边通分,得 分母为(x+2)(x+3),分子为Ax+3A+Bx+2B=(A+B)x+3A+2B.
∴3x+5=(A+B)x+3A+2B.
即A+B=3,3A+2B=5.
解之得 A=-1,B=4
∴所求式子为 【3×(-1)+4】^2008=1^2008=1.
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