Whakaoti i te 1+frac{1/1+frac{1{2}}}{1-1/1-frac{1{2}}}-2*3/4-2frac{3/4}{1+frac{1}{1-frac{3}{4}}}

$$\frac { 1 + \frac { 1 } { 1 + \frac { 1 } { 2 } } } { 1 - \frac { 1 } { 1 - \frac { 1 } { 2 } } } - \frac { 2 \cdot \frac { 3 } { 4 } - 2 \frac { 3 } { 4 } } { 1 + \frac { 1 } { 1 - \frac { 3 } { 4 } } }$$

Aromātai

$$-\frac{17}{12}\approx -1.416666667$$

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{2}{2}.

$$\frac{1+\frac{1}{\frac{2}{2}+\frac{1}{2}}}{1-\frac{1}{1-\frac{1}{2}}}-\frac{2\times \frac{3}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Tā te mea he rite te tauraro o \frac{2}{2} me \frac{1}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1+\frac{1}{\frac{2+1}{2}}}{1-\frac{1}{1-\frac{1}{2}}}-\frac{2\times \frac{3}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{1+\frac{1}{\frac{3}{2}}}{1-\frac{1}{1-\frac{1}{2}}}-\frac{2\times \frac{3}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Whakawehe 1 ki te \frac{3}{2} mā te whakarea 1 ki te tau huripoki o \frac{3}{2}.

$$\frac{1+1\times \frac{2}{3}}{1-\frac{1}{1-\frac{1}{2}}}-\frac{2\times \frac{3}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

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

$$\frac{1+\frac{2}{3}}{1-\frac{1}{1-\frac{1}{2}}}-\frac{2\times \frac{3}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Me tahuri te 1 ki te hautau \frac{3}{3}.

$$\frac{\frac{3}{3}+\frac{2}{3}}{1-\frac{1}{1-\frac{1}{2}}}-\frac{2\times \frac{3}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Tā te mea he rite te tauraro o \frac{3}{3} me \frac{2}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{3+2}{3}}{1-\frac{1}{1-\frac{1}{2}}}-\frac{2\times \frac{3}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Tāpirihia te 3 ki te 2, ka 5.

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

Me tahuri te 1 ki te hautau \frac{2}{2}.

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

Tā te mea he rite te tauraro o \frac{2}{2} me \frac{1}{2}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 2, ka 1.

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

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

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

Whakareatia te 1 ki te 2, ka 2.

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

Tangohia te 2 i te 1, ka -1.

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

Tuhia te \frac{\frac{5}{3}}{-1} hei hautanga kotahi.

$$\frac{5}{3\left(-1\right)}-\frac{2\times \frac{3}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Whakareatia te 3 ki te -1, ka -3.

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

Ka taea te hautanga \frac{5}{-3} te tuhi anō ko -\frac{5}{3} mā te tango i te tohu tōraro.

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

Tuhia te 2\times \frac{3}{4} hei hautanga kotahi.

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

Whakareatia te 2 ki te 3, ka 6.

$$-\frac{5}{3}-\frac{\frac{6}{4}-\frac{2\times 4+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Whakahekea te hautanga \frac{6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Whakareatia te 2 ki te 4, ka 8.

$$-\frac{5}{3}-\frac{\frac{3}{2}-\frac{8+3}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Tāpirihia te 8 ki te 3, ka 11.

$$-\frac{5}{3}-\frac{\frac{3}{2}-\frac{11}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Ko te maha noa iti rawa atu o 2 me 4 ko 4. Me tahuri \frac{3}{2} me \frac{11}{4} ki te hautau me te tautūnga 4.

$$-\frac{5}{3}-\frac{\frac{6}{4}-\frac{11}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Tā te mea he rite te tauraro o \frac{6}{4} me \frac{11}{4}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{5}{3}-\frac{\frac{6-11}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

Tangohia te 11 i te 6, ka -5.

$$-\frac{5}{3}-\frac{-\frac{5}{4}}{1+\frac{1}{1-\frac{3}{4}}}$$

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

$$-\frac{5}{3}-\frac{-\frac{5}{4}}{1+\frac{1}{\frac{4}{4}-\frac{3}{4}}}$$

Tā te mea he rite te tauraro o \frac{4}{4} me \frac{3}{4}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{5}{3}-\frac{-\frac{5}{4}}{1+\frac{1}{\frac{4-3}{4}}}$$

Tangohia te 3 i te 4, ka 1.

$$-\frac{5}{3}-\frac{-\frac{5}{4}}{1+\frac{1}{\frac{1}{4}}}$$

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

$$-\frac{5}{3}-\frac{-\frac{5}{4}}{1+1\times 4}$$

Whakareatia te 1 ki te 4, ka 4.

$$-\frac{5}{3}-\frac{-\frac{5}{4}}{1+4}$$

Tāpirihia te 1 ki te 4, ka 5.

$$-\frac{5}{3}-\frac{-\frac{5}{4}}{5}$$

Tuhia te \frac{-\frac{5}{4}}{5} hei hautanga kotahi.

$$-\frac{5}{3}-\frac{-5}{4\times 5}$$

Whakareatia te 4 ki te 5, ka 20.

$$-\frac{5}{3}-\frac{-5}{20}$$

Whakahekea te hautanga \frac{-5}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$-\frac{5}{3}-\left(-\frac{1}{4}\right)$$

Ko te tauaro o -\frac{1}{4} ko \frac{1}{4}.

$$-\frac{5}{3}+\frac{1}{4}$$

Ko te maha noa iti rawa atu o 3 me 4 ko 12. Me tahuri -\frac{5}{3} me \frac{1}{4} ki te hautau me te tautūnga 12.

$$-\frac{20}{12}+\frac{3}{12}$$

Tā te mea he rite te tauraro o -\frac{20}{12} me \frac{3}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-20+3}{12}$$

Tāpirihia te -20 ki te 3, ka -17.

$$-\frac{17}{12}$$

Tauwehe

$$-\frac{17}{12} = -1\frac{5}{12} = -1.4166666666666667$$