Whakaoti i te 71/15+left(x-7right)left(1/15+1/12right)=1

$$7 \frac{ 1 }{ 15 } + \left( x-7 \right) \left( \frac{ 1 }{ 15 } + \frac{ 1 }{ 12 } \right) = 1$$

Whakaoti mō x

$$x = -\frac{301}{9} = -33\frac{4}{9} \approx -33.444444444$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 60, arā, te tauraro pātahi he tino iti rawa te kitea o 15,12.

$$4\left(7\times 15+1\right)+60\left(x-7\right)\left(\frac{1}{15}+\frac{1}{12}\right)=60$$

Whakareatia te 7 ki te 15, ka 105.

$$4\left(105+1\right)+60\left(x-7\right)\left(\frac{1}{15}+\frac{1}{12}\right)=60$$

Tāpirihia te 105 ki te 1, ka 106.

$$4\times 106+60\left(x-7\right)\left(\frac{1}{15}+\frac{1}{12}\right)=60$$

Whakareatia te 4 ki te 106, ka 424.

$$424+60\left(x-7\right)\left(\frac{1}{15}+\frac{1}{12}\right)=60$$

Ko te maha noa iti rawa atu o 15 me 12 ko 60. Me tahuri \frac{1}{15} me \frac{1}{12} ki te hautau me te tautūnga 60.

$$424+60\left(x-7\right)\left(\frac{4}{60}+\frac{5}{60}\right)=60$$

Tā te mea he rite te tauraro o \frac{4}{60} me \frac{5}{60}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$424+60\left(x-7\right)\times \frac{4+5}{60}=60$$

Tāpirihia te 4 ki te 5, ka 9.

$$424+60\left(x-7\right)\times \frac{9}{60}=60$$

Whakahekea te hautanga \frac{9}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$424+60\left(x-7\right)\times \frac{3}{20}=60$$

Tuhia te 60\times \frac{3}{20} hei hautanga kotahi.

$$424+\frac{60\times 3}{20}\left(x-7\right)=60$$

Whakareatia te 60 ki te 3, ka 180.

$$424+\frac{180}{20}\left(x-7\right)=60$$

Whakawehea te 180 ki te 20, kia riro ko 9.

$$424+9\left(x-7\right)=60$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te x-7.

$$424+9x-63=60$$

Tangohia te 63 i te 424, ka 361.

$$361+9x=60$$

Tangohia te 361 mai i ngā taha e rua.

$$9x=60-361$$

Tangohia te 361 i te 60, ka -301.

$$9x=-301$$

Whakawehea ngā taha e rua ki te 9.

$$x=\frac{-301}{9}$$

Ka taea te hautanga \frac{-301}{9} te tuhi anō ko -\frac{301}{9} mā te tango i te tohu tōraro.

$$x=-\frac{301}{9}$$