Whakaoti i te x=2+frac{1/3frac{4{5}}}{2+1/3+1{1+frac{1/4}}}

$$x = \frac { 2 + \frac { 1 } { 3 \frac { 4 } { 5 } } } { 2 + \frac { 1 } { 3 + \frac { 1 } { 1 + \frac { 1 } { 4 } } } }$$

Whakaoti mō x

$$x=1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawehe 1 ki te \frac{3\times 5+4}{5} mā te whakarea 1 ki te tau huripoki o \frac{3\times 5+4}{5}.

$$x=\frac{2+\frac{5}{3\times 5+4}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Whakareatia te 3 ki te 5, ka 15.

$$x=\frac{2+\frac{5}{15+4}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Tāpirihia te 15 ki te 4, ka 19.

$$x=\frac{2+\frac{5}{19}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Me tahuri te 2 ki te hautau \frac{38}{19}.

$$x=\frac{\frac{38}{19}+\frac{5}{19}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Tā te mea he rite te tauraro o \frac{38}{19} me \frac{5}{19}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{\frac{38+5}{19}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Tāpirihia te 38 ki te 5, ka 43.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Me tahuri te 1 ki te hautau \frac{4}{4}.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{1}{\frac{4}{4}+\frac{1}{4}}}}$$

Tā te mea he rite te tauraro o \frac{4}{4} me \frac{1}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{1}{\frac{4+1}{4}}}}$$

Tāpirihia te 4 ki te 1, ka 5.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{1}{\frac{5}{4}}}}$$

Whakawehe 1 ki te \frac{5}{4} mā te whakarea 1 ki te tau huripoki o \frac{5}{4}.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+1\times \frac{4}{5}}}$$

Whakareatia te 1 ki te \frac{4}{5}, ka \frac{4}{5}.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{4}{5}}}$$

Me tahuri te 3 ki te hautau \frac{15}{5}.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{\frac{15}{5}+\frac{4}{5}}}$$

Tā te mea he rite te tauraro o \frac{15}{5} me \frac{4}{5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{\frac{15+4}{5}}}$$

Tāpirihia te 15 ki te 4, ka 19.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{\frac{19}{5}}}$$

Whakawehe 1 ki te \frac{19}{5} mā te whakarea 1 ki te tau huripoki o \frac{19}{5}.

$$x=\frac{\frac{43}{19}}{2+1\times \frac{5}{19}}$$

Whakareatia te 1 ki te \frac{5}{19}, ka \frac{5}{19}.

$$x=\frac{\frac{43}{19}}{2+\frac{5}{19}}$$

Me tahuri te 2 ki te hautau \frac{38}{19}.

$$x=\frac{\frac{43}{19}}{\frac{38}{19}+\frac{5}{19}}$$

Tā te mea he rite te tauraro o \frac{38}{19} me \frac{5}{19}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{\frac{43}{19}}{\frac{38+5}{19}}$$

Tāpirihia te 38 ki te 5, ka 43.

$$x=\frac{\frac{43}{19}}{\frac{43}{19}}$$

Whakawehea te \frac{43}{19} ki te \frac{43}{19}, kia riro ko 1.

$$x=1$$

Tautapa x

$$x≔1$$