Whakaoti i te {l}{(985/466+466/985+899/394)*(769/347+frac{689}{423})}{-(frac{760}{347}+frac{689}{423}+frac{985}{467})*(frac{466}{985}+frac{699}{394})}

$$\left. \begin{array} { l } { ( \frac { 985 } { 466 } + \frac { 466 } { 985 } + \frac { 899 } { 394 } ) \times ( \frac { 769 } { 347 } + \frac { 689 } { 423 } ) } \\ { - ( \frac { 760 } { 347 } + \frac { 689 } { 423 } + \frac { 985 } { 467 } ) \times ( \frac { 466 } { 985 } + \frac { 699 } { 394 } ) } \end{array} \right.$$

Aromātai

$$\frac{28304092692749}{5243938860045}\approx 5.397487165$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 466 me 985 ko 459010. Me tahuri \frac{985}{466} me \frac{466}{985} ki te hautau me te tautūnga 459010.

$$\left(\frac{970225}{459010}+\frac{217156}{459010}+\frac{899}{394}\right)\left(\frac{769}{347}+\frac{689}{423}\right)-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tā te mea he rite te tauraro o \frac{970225}{459010} me \frac{217156}{459010}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\left(\frac{970225+217156}{459010}+\frac{899}{394}\right)\left(\frac{769}{347}+\frac{689}{423}\right)-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tāpirihia te 970225 ki te 217156, ka 1187381.

$$\left(\frac{1187381}{459010}+\frac{899}{394}\right)\left(\frac{769}{347}+\frac{689}{423}\right)-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Ko te maha noa iti rawa atu o 459010 me 394 ko 459010. Me tahuri \frac{1187381}{459010} me \frac{899}{394} ki te hautau me te tautūnga 459010.

$$\left(\frac{1187381}{459010}+\frac{1047335}{459010}\right)\left(\frac{769}{347}+\frac{689}{423}\right)-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tā te mea he rite te tauraro o \frac{1187381}{459010} me \frac{1047335}{459010}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1187381+1047335}{459010}\left(\frac{769}{347}+\frac{689}{423}\right)-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tāpirihia te 1187381 ki te 1047335, ka 2234716.

$$\frac{2234716}{459010}\left(\frac{769}{347}+\frac{689}{423}\right)-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Whakahekea te hautanga \frac{2234716}{459010} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1117358}{229505}\left(\frac{769}{347}+\frac{689}{423}\right)-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Ko te maha noa iti rawa atu o 347 me 423 ko 146781. Me tahuri \frac{769}{347} me \frac{689}{423} ki te hautau me te tautūnga 146781.

$$\frac{1117358}{229505}\left(\frac{325287}{146781}+\frac{239083}{146781}\right)-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tā te mea he rite te tauraro o \frac{325287}{146781} me \frac{239083}{146781}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1117358}{229505}\times \frac{325287+239083}{146781}-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tāpirihia te 325287 ki te 239083, ka 564370.

$$\frac{1117358}{229505}\times \frac{564370}{146781}-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Me whakarea te \frac{1117358}{229505} ki te \frac{564370}{146781} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1117358\times 564370}{229505\times 146781}-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{1117358\times 564370}{229505\times 146781}.

$$\frac{630603334460}{33686973405}-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Whakahekea te hautanga \frac{630603334460}{33686973405} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{126120666892}{6737394681}-\left(\frac{760}{347}+\frac{689}{423}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Ko te maha noa iti rawa atu o 347 me 423 ko 146781. Me tahuri \frac{760}{347} me \frac{689}{423} ki te hautau me te tautūnga 146781.

$$\frac{126120666892}{6737394681}-\left(\frac{321480}{146781}+\frac{239083}{146781}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tā te mea he rite te tauraro o \frac{321480}{146781} me \frac{239083}{146781}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{126120666892}{6737394681}-\left(\frac{321480+239083}{146781}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tāpirihia te 321480 ki te 239083, ka 560563.

$$\frac{126120666892}{6737394681}-\left(\frac{560563}{146781}+\frac{985}{467}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Ko te maha noa iti rawa atu o 146781 me 467 ko 68546727. Me tahuri \frac{560563}{146781} me \frac{985}{467} ki te hautau me te tautūnga 68546727.

$$\frac{126120666892}{6737394681}-\left(\frac{261782921}{68546727}+\frac{144579285}{68546727}\right)\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tā te mea he rite te tauraro o \frac{261782921}{68546727} me \frac{144579285}{68546727}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{126120666892}{6737394681}-\frac{261782921+144579285}{68546727}\left(\frac{466}{985}+\frac{699}{394}\right)$$

Tāpirihia te 261782921 ki te 144579285, ka 406362206.

$$\frac{126120666892}{6737394681}-\frac{406362206}{68546727}\left(\frac{466}{985}+\frac{699}{394}\right)$$

Ko te maha noa iti rawa atu o 985 me 394 ko 1970. Me tahuri \frac{466}{985} me \frac{699}{394} ki te hautau me te tautūnga 1970.

$$\frac{126120666892}{6737394681}-\frac{406362206}{68546727}\left(\frac{932}{1970}+\frac{3495}{1970}\right)$$

Tā te mea he rite te tauraro o \frac{932}{1970} me \frac{3495}{1970}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{126120666892}{6737394681}-\frac{406362206}{68546727}\times \frac{932+3495}{1970}$$

Tāpirihia te 932 ki te 3495, ka 4427.

$$\frac{126120666892}{6737394681}-\frac{406362206}{68546727}\times \frac{4427}{1970}$$

Me whakarea te \frac{406362206}{68546727} ki te \frac{4427}{1970} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{126120666892}{6737394681}-\frac{406362206\times 4427}{68546727\times 1970}$$

Mahia ngā whakarea i roto i te hautanga \frac{406362206\times 4427}{68546727\times 1970}.

$$\frac{126120666892}{6737394681}-\frac{1798965485962}{135037052190}$$

Whakahekea te hautanga \frac{1798965485962}{135037052190} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{126120666892}{6737394681}-\frac{899482742981}{67518526095}$$

Ko te maha noa iti rawa atu o 6737394681 me 67518526095 ko 15731816580135. Me tahuri \frac{126120666892}{6737394681} me \frac{899482742981}{67518526095} ki te hautau me te tautūnga 15731816580135.

$$\frac{294491757192820}{15731816580135}-\frac{209579479114573}{15731816580135}$$

Tā te mea he rite te tauraro o \frac{294491757192820}{15731816580135} me \frac{209579479114573}{15731816580135}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{294491757192820-209579479114573}{15731816580135}$$

Tangohia te 209579479114573 i te 294491757192820, ka 84912278078247.

$$\frac{84912278078247}{15731816580135}$$

Whakahekea te hautanga \frac{84912278078247}{15731816580135} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{28304092692749}{5243938860045}$$

Tauwehe

$$\frac{28304092692749}{3 \cdot 5 \cdot 47 \cdot 197 \cdot 233 \cdot 347 \cdot 467} = 5\frac{2084398392524}{5243938860045} = 5.397487165307284$$