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