Whakaoti i te a/2+2/3=3a/5+5/7

$$\frac { a } { 2 } + \frac { 2 } { 3 } = \frac { 3 a } { 5 } + \frac { 5 } { 7 }$$

Whakaoti mō a

$$a=-\frac{10}{21}\approx -0.476190476$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 210, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3,5,7.

$$105a+140=42\times 3a+150$$

Whakareatia te 42 ki te 3, ka 126.

$$105a+140=126a+150$$

Tangohia te 126a mai i ngā taha e rua.

$$105a+140-126a=150$$

Pahekotia te 105a me -126a, ka -21a.

$$-21a+140=150$$

Tangohia te 140 mai i ngā taha e rua.

$$-21a=150-140$$

Tangohia te 140 i te 150, ka 10.

$$-21a=10$$

Whakawehea ngā taha e rua ki te -21.

$$a=\frac{10}{-21}$$

Ka taea te hautanga \frac{10}{-21} te tuhi anō ko -\frac{10}{21} mā te tango i te tohu tōraro.

$$a=-\frac{10}{21}$$