解分式方程(5-2x)/(x^2-x-12)=5x/(x^2+x-6)+(10-7x)/(x^2-6x+8)得

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解分式方程(5-2x)/(x^2-x-12)=5x/(x^2+x-6)+(10-7x)/(x^2-6x+8)得
解分式方程(5-2x)/(x^2-x-12)=5x/(x^2+x-6)+(10-7x)/(x^2-6x+8)得

解分式方程(5-2x)/(x^2-x-12)=5x/(x^2+x-6)+(10-7x)/(x^2-6x+8)得
(5-2x)/(x^2-x-12)=5x/(x^2+x-6)+(10-7x)/(x^2-6x+8)
(5-2x)/(x-4)(x+3)=5x/(x+3)(x-2)+(10-7x)/(x-2)(x-4)
分母同时乘以(x-4)(x+3)(x-2)得
(5-2x)(x-2)=5x(x-4)+(10-7x)(x+3)
即-2x^2+9x-10=5x^2-20x-7x^2-11x+30
9x-10=-31x+30
40x=40
x=1

(5-2x)/(x^2-x-12)=5x/(x^2+x-6)+(10-7x)/(x^2-6x+8)
(5-2x)/{(x+3)(x-4)} = 5x/{(x+3)(x-2)} + (10-7x) / {(x-2)(x-4)}
(5-2x)/{(x+3)(x-4)} - 5x/{(x+3)(x-2)} - (10-7x) / {(x-2)(x-4)} = 0
{ (5-2x...

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(5-2x)/(x^2-x-12)=5x/(x^2+x-6)+(10-7x)/(x^2-6x+8)
(5-2x)/{(x+3)(x-4)} = 5x/{(x+3)(x-2)} + (10-7x) / {(x-2)(x-4)}
(5-2x)/{(x+3)(x-4)} - 5x/{(x+3)(x-2)} - (10-7x) / {(x-2)(x-4)} = 0
{ (5-2x)(x-2) - 5x(x-4) - (10-7x)(x+3) } / {(x+3)(x-2)(x-4)} = 0
{ (-2x^2+9x-10) - (5x^2-20x) - (-7x^2-11x+30) } / {(x+3)(x-2)(x-4)} = 0
{ -2x^2+9x-10 - 5x^2 + 20x + 7x^2 +11x - 30) } / {(x+3)(x-2)(x-4)} = 0
40(x-1) / {(x+3)(x-2)(x-4)} = 0
x=1

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