Whakaoti i te (1+1/2+1/3)(x-2/frac{1{2}-1/3}+1)=1+2^-1+3^-1

$$( 1 + \frac { 1 } { 2 } + \frac { 1 } { 3 } ) ( \frac { x - 2 } { \frac { 1 } { 2 } - \frac { 1 } { 3 } } + 1 ) = 1 + 2 ^ { - 1 } + 3 ^ { - 1 }$$

Whakaoti mō x

$$x=2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tāpirihia te 1 ki te \frac{1}{2}, ka \frac{3}{2}.

$$\left(\frac{3}{2}+\frac{1}{3}\right)\left(\frac{x-2}{\frac{1}{2}-\frac{1}{3}}+1\right)=1+2^{-1}+3^{-1}$$

Tāpirihia te \frac{3}{2} ki te \frac{1}{3}, ka \frac{11}{6}.

$$\frac{11}{6}\left(\frac{x-2}{\frac{1}{2}-\frac{1}{3}}+1\right)=1+2^{-1}+3^{-1}$$

Tangohia te \frac{1}{3} i te \frac{1}{2}, ka \frac{1}{6}.

$$\frac{11}{6}\left(\frac{x-2}{\frac{1}{6}}+1\right)=1+2^{-1}+3^{-1}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{11}{6} ki te \frac{x-2}{\frac{1}{6}}+1.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=1+2^{-1}+3^{-1}$$

Tātaihia te 2 mā te pū o -1, kia riro ko \frac{1}{2}.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=1+\frac{1}{2}+3^{-1}$$

Tāpirihia te 1 ki te \frac{1}{2}, ka \frac{3}{2}.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{3}{2}+3^{-1}$$

Tātaihia te 3 mā te pū o -1, kia riro ko \frac{1}{3}.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{3}{2}+\frac{1}{3}$$

Tāpirihia te \frac{3}{2} ki te \frac{1}{3}, ka \frac{11}{6}.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{11}{6}$$

Whakawehea ia wā o x-2 ki te \frac{1}{6}, kia riro ko \frac{x}{\frac{1}{6}}+\frac{-2}{\frac{1}{6}}.

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}+\frac{-2}{\frac{1}{6}}\right)+\frac{11}{6}=\frac{11}{6}$$

Whakawehe -2 ki te \frac{1}{6} mā te whakarea -2 ki te tau huripoki o \frac{1}{6}.

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}-2\times 6\right)+\frac{11}{6}=\frac{11}{6}$$

Whakareatia te -2 ki te 6, ka -12.

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}-12\right)+\frac{11}{6}=\frac{11}{6}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{11}{6} ki te \frac{x}{\frac{1}{6}}-12.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}-22+\frac{11}{6}=\frac{11}{6}$$

Tāpirihia te -22 ki te \frac{11}{6}, ka -\frac{121}{6}.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}-\frac{121}{6}=\frac{11}{6}$$

Me tāpiri te \frac{121}{6} ki ngā taha e rua.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}=\frac{11}{6}+\frac{121}{6}$$

Tāpirihia te \frac{11}{6} ki te \frac{121}{6}, ka 22.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}=22$$

Me whakarea ngā taha e rua ki te \frac{6}{11}, te tau utu o \frac{11}{6}.

$$\frac{x}{\frac{1}{6}}=22\times \frac{6}{11}$$

Whakareatia te 22 ki te \frac{6}{11}, ka 12.

$$\frac{x}{\frac{1}{6}}=12$$

Me whakarea ngā taha e rua ki te \frac{1}{6}.

$$x=12\times \frac{1}{6}$$

Whakareatia te 12 ki te \frac{1}{6}, ka 2.

$$x=2$$