5/(x^2-x-6) - 6/(x^2-4)=4/(x^2-5x+6)

题目

5/(x^2-x-6) - 6/(x^2-4)=4/(x^2-5x+6)

答案

5/(x-3)(x+2) -6/(x+2)(x-2)=4/(x-2)(x-3)
两边乘以(x-3)(x+2)(x-2)得
5(x-2)-6(x-3)=4(x+2)
5x-10-6x+18=4x+8
-5x=20
x=-4
检验：x=-4是方程的解