字母求值题来的若x-1/(x^2-5x+6)=a/(x-2)+b/(x-3)则a=______,b=_______

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字母求值题来的若x-1/(x^2-5x+6)=a/(x-2)+b/(x-3)则a=______,b=_______

字母求值题来的若x-1/(x^2-5x+6)=a/(x-2)+b/(x-3)则a=______,b=_______
字母求值题来的
若x-1/(x^2-5x+6)=a/(x-2)+b/(x-3)
则a=______,b=_______

字母求值题来的若x-1/(x^2-5x+6)=a/(x-2)+b/(x-3)则a=______,b=_______
(x-1)/(x^2-5x+6)=a/(x-2)+b/(x-3)=[a(x-3)+b(x-2)]/(x^2-5x+6)
所以x-1=ax-3a+bx-2b=(a+b)x-(3a+2b)
所以a+b=1,-(3a+2b)=-1
a=-1,b=2

x-1/(x-2)*(x-3)=a/(x-2)+b/(x-3)
两边乘以(x-2)*(x-3)
x-1=a(x-3)+b*(x-2)
(a+b-1)x=3a+2b-1
x=3a+2b-1/(a+b-1)

将等式右边通分得
(x-1)/(x^2-5x+6)=a/(x-2)+b/(x-3)=[a(x-3)+b(x-2)]/(x^2-5x+6)
因为分母相等,所以
x-1=a(x-3)+b(x-2)=(a+b)x-(3a+2b)
所以a+b=1,3a+2b=1
所以a=-1,b=2