x减7分之x减5加x减4分之x减2等于x减5分之x减3加x减6分之x减4解方程

Question

x减7分之x减5 加x减4分之x减2等于x减5分之x减3加x减6分之x减4
解方程

Answer 1

(x-5)/(x-7)+(x-2)/(x-4)=(x-3)/(x-5)+(x-4)/(x-6)
[(x-5)(x-4)+(x-2)(x-7)]/(x-7)(x-4)=[(x-3)(x-6)+(x-4)(x-5)]/(x-5)(x-6)
(x²-9x+20+x²-9x+14)/(x²-11x+28)=(x²-9x+18+x²-9x+20)/(x²-11x+30)
(2x²-18x+34)/(x²-11x+28)=(2x²-18x+38)/(x²-11x+30)
2(x²-9x+17)(x²-11x+30)=2(x²-9x+19)(x²-11x+28)
(x²-9x)(x²-11x)+17(x²-11x)+30(x²-9x)+510=(x²-9x)(x²-11x)+19(x²-11x)+28(x²-9x)+532
-2(x²-11x)+2(x²-9x)-22=0
-2x²+22x+2x²-18x-22=0
4x=22
∴x=5.5