解: ( 1/9 *x+1)÷(x-1)=3/22
22x/9+22=3x-3
(3-22/9)x=22+3
(27-22)/9*x=25
5/9 *x=25
x=25*9/5
x=45
经检验x=45是原方程的根.
(1/9×x+1)÷(x-1)=3/22
1/9x+1=3/22×(x-1)
1/9x+1=3/22x-3/22
1/9x-3/22x=-1-3/22
(22×1)/(22×9)x-(9×3)/(9×22)x=-22/22-3/22
22/198x-27/198x=-(22/22+3/22)
-5/198x=-25/22
-5/198x×(-198)=-25/22×(-198)
5x=25×9
x=25×9÷5
x=5×9
x=45
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