Whakaoti i te 30-37/40-x=37-50/x-45

$$\frac{ 30-37 }{ 40-x } = \frac{ 37-50 }{ x-45 }$$

Whakaoti mō x

$$x = \frac{167}{4} = 41\frac{3}{4} = 41.75$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 40,45 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-45\right)\left(x-40\right), arā, te tauraro pātahi he tino iti rawa te kitea o 40-x,x-45.

$$\left(45-x\right)\left(30-37\right)=\left(x-40\right)\left(37-50\right)$$

Tangohia te 37 i te 30, ka -7.

$$\left(45-x\right)\left(-7\right)=\left(x-40\right)\left(37-50\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 45-x ki te -7.

$$-315+7x=\left(x-40\right)\left(37-50\right)$$

Tangohia te 50 i te 37, ka -13.

$$-315+7x=\left(x-40\right)\left(-13\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-40 ki te -13.

$$-315+7x=-13x+520$$

Me tāpiri te 13x ki ngā taha e rua.

$$-315+7x+13x=520$$

Pahekotia te 7x me 13x, ka 20x.

$$-315+20x=520$$

Me tāpiri te 315 ki ngā taha e rua.

$$20x=520+315$$

Tāpirihia te 520 ki te 315, ka 835.

$$20x=835$$

Whakawehea ngā taha e rua ki te 20.

$$x=\frac{835}{20}$$

Whakahekea te hautanga \frac{835}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x=\frac{167}{4}$$