Question

解分式方程（X-4)/(X-5)-(X-5)/(X-6)=(X-7)/(X-8)-(X-8)/(X-9)

Answer 1

左右两边同乘以(X-5)(X-6)(X-8)(X-9)
得到(X-4)(X-6)(X-8)(X-9)-(X-5)(X-5)(X-8)(X-9)=(X-5)(X-6)(X-7)(X-9)-(X-5)(X-6)(X-8)(X-8)
整理得到-(X-8)(X-9)=-(X-5)(X-6)
展开解得X=7

Answer 2

设y=x-5，则方程左边为(y+1)/y-y/(y-1)=-1/(y²-y)=-1/(x²-11x+30)
色z=x-8，则方程右边为(z+1)/z-z/(z-1)=-1/(z²-z)=-1/(x²-17x+72)
左边=右边
-1/(x²-11x+30)=-1/(x²-17x+72)
即x²-11x+30=x²-17x+72
得x=7。