Whakaoti i te 3/2=6-x+10/x-3

$$\frac { 3 } { 2 } = 6 - \frac { x + 10 } { x - 3 }$$

Whakaoti mō x

$$x = \frac{47}{7} = 6\frac{5}{7} \approx 6.714285714$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2\left(x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2,x-3.

$$3\left(x-3\right)=2\left(x-3\right)\times 6-2\left(x+10\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x-3.

$$3x-9=2\left(x-3\right)\times 6-2\left(x+10\right)$$

Whakareatia te 2 ki te 6, ka 12.

$$3x-9=12\left(x-3\right)-2\left(x+10\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 12 ki te x-3.

$$3x-9=12x-36-2\left(x+10\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x+10.

$$3x-9=12x-36-2x-20$$

Pahekotia te 12x me -2x, ka 10x.

$$3x-9=10x-36-20$$

Tangohia te 20 i te -36, ka -56.

$$3x-9=10x-56$$

Tangohia te 10x mai i ngā taha e rua.

$$3x-9-10x=-56$$

Pahekotia te 3x me -10x, ka -7x.

$$-7x-9=-56$$

Me tāpiri te 9 ki ngā taha e rua.

$$-7x=-56+9$$

Tāpirihia te -56 ki te 9, ka -47.

$$-7x=-47$$

Whakawehea ngā taha e rua ki te -7.

$$x=\frac{-47}{-7}$$

Ka taea te hautanga \frac{-47}{-7} te whakamāmā ki te \frac{47}{7} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{47}{7}$$