题目

计算下列分式,
1/(x-10)+1/x=1/12
1+1200/(x+100)=1200/x

提问时间：2021-01-14

答案

x/x(x-10)+(x-10)/x(x-10)=1/12
(2x-10)/x(x-10)=1/12
x(x-10)=12(2x-10)
x^2-10x=24x-120
x^2-34x+120=0
(x-30)(x-4)=0
x1=30,x2=4
[(x+100)+1200]/(x+100)=1200/x
1200(x+100)=x(x+1300)
x^2+6300x=1200x+120000
x^2+100x=120000
(x-300)(x+400)=0
x1=300,x2=-400