Question

解分式方程：(5x-96)/(x-19)+(x-8)/(x-9)=(4x-19)/(x-6)+(2x-21)/(x-8) 要过程，谢了

Answer 1

(5x-96)/(x-19)+(x-8)/(x-9)=(4x-19)/(x-6)+(2x-21)/(x-8)
5-1/(x-19)+1+1/(x-9)=4+5/(x-6)+2-5/(x-8)
即 1/(x-9)-1/(x-19)=5/(x-6)-5/(x-8)
-10/[(x-9)(x-19)]=-10/[(x-6)(x-8)]
则 1/[(x-9)(x-19)]=1/[(x-6)(x-8)]
即 (x-6)(x-8)=(x-9)(x-19)
x²-14x+48=x²-28x+171
14x=123
得 x=123/14

Answer 2

解分式方程：(5x-96)/(x-19)+(x-8)/(x-9)=(4x-19)/(x-6)+(2x-21)/(x-8) 要过程，

(5x-96)/(x-19)+(x-8)/(x-9)=(4x-19)/(x-6)+(2x-21)/(x-8)
[(5x-96)(x-9)+(x-8)(x-19)]/(x-19)(x-9)=[(4x-19)(x-8)+(2x-21)(x-6)]/(x-6)(x-8)
(6x²-168x+1016)/(x²-28x+171)=(6x²-84x+278)/(x²-14x+48)
(6x²-168x+1026-10)/(x²-28x+171)=(6x²-84x+288-10)/(x²-14x+48)
6-10/(x²-28x+171)=6-10/(x²-14x+48)
10/(x²-28x+171)=10/(x²-14x+48)
x²-28x+171=x²-14x+48
-28x+171=-14x+48
14x=123
x=123/14