Question

计算下列分式,1/(x-10)+1/x=1/121+1200/(x+100)=1200/x

Answer 1

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