若x-5分之A+x+2分之B=x平方-3x-10分之5x-4,试求A,B的值
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若(x-5)分之A+(x+2)分之B=(x²-3x-10)分之(5x-4),试求A,B的值
A/(x-5)+B/(x+2)=(5x-4)/(x²-3x-10),
(x+2)A/[(x-5)(x+2)]+(x-5)B/[(x+2)(x-5)]=(5x-4)/(x²-3x-10),
[(x+2)A+(x-5)B]/(x²-5x+2x-10)=(5x-4)/(x²-3x-10),
(Ax+2A+Bx-5B)/(x²-3x-10)=(5x-4)/(x²-3x-10),
[(A+B)x+2A-5B]/(x²-3x-10)=(5x-4)/(x²-3x-10),
所以:
A+B=5,
2A-5B=-4,
解方程组:
A=3,
B=2
A/(x-5)+B/(x+2)=(5x-4)/(x²-3x-10),
(x+2)A/[(x-5)(x+2)]+(x-5)B/[(x+2)(x-5)]=(5x-4)/(x²-3x-10),
[(x+2)A+(x-5)B]/(x²-5x+2x-10)=(5x-4)/(x²-3x-10),
(Ax+2A+Bx-5B)/(x²-3x-10)=(5x-4)/(x²-3x-10),
[(A+B)x+2A-5B]/(x²-3x-10)=(5x-4)/(x²-3x-10),
所以:
A+B=5,
2A-5B=-4,
解方程组:
A=3,
B=2
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