Whakaoti i te 2x-(7-5x)/9x-(3+4x)=7/6f

$$\frac { 2 x - ( 7 - 5 x ) } { 9 x - ( 3 + 4 x ) } = \frac { 7 } { 6 } f$$

Whakaoti mō f

$$f=-\frac{6\left(x-1\right)}{3-5x}$$

$$x\neq \frac{3}{5}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 6\left(5x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 9x-\left(3+4x\right),6.

$$6\left(2x-\left(7-5x\right)\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

Hei kimi i te tauaro o 7-5x, kimihia te tauaro o ia taurangi.

$$6\left(2x-7+5x\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

Pahekotia te 2x me 5x, ka 7x.

$$6\left(7x-7\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te 7x-7.

$$42x-42=\frac{7}{6}f\times 6\left(5x-3\right)$$

Whakareatia te \frac{7}{6} ki te 6, ka 7.

$$42x-42=7f\left(5x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7f ki te 5x-3.

$$42x-42=35xf-21f$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$35xf-21f=42x-42$$

Pahekotia ngā kīanga tau katoa e whai ana i te f.

$$\left(35x-21\right)f=42x-42$$

Whakawehea ngā taha e rua ki te 35x-21.

$$\frac{\left(35x-21\right)f}{35x-21}=\frac{42x-42}{35x-21}$$

Mā te whakawehe ki te 35x-21 ka wetekia te whakareanga ki te 35x-21.

$$f=\frac{42x-42}{35x-21}$$

Whakawehe -42+42x ki te 35x-21.

$$f=\frac{6\left(x-1\right)}{5x-3}$$

Whakaoti mō x

$$x=-\frac{3\left(f-2\right)}{6-5f}$$

$$f\neq \frac{6}{5}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki \frac{3}{5} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 6\left(5x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 9x-\left(3+4x\right),6.

$$6\left(2x-\left(7-5x\right)\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

Hei kimi i te tauaro o 7-5x, kimihia te tauaro o ia taurangi.

$$6\left(2x-7+5x\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

Pahekotia te 2x me 5x, ka 7x.

$$6\left(7x-7\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te 7x-7.

$$42x-42=\frac{7}{6}f\times 6\left(5x-3\right)$$

Whakareatia te \frac{7}{6} ki te 6, ka 7.

$$42x-42=7f\left(5x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7f ki te 5x-3.

$$42x-42=35fx-21f$$

Tangohia te 35fx mai i ngā taha e rua.

$$42x-42-35fx=-21f$$

Me tāpiri te 42 ki ngā taha e rua.

$$42x-35fx=-21f+42$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(42-35f\right)x=-21f+42$$

He hanga arowhānui tō te whārite.

$$\left(42-35f\right)x=42-21f$$

Whakawehea ngā taha e rua ki te 42-35f.

$$\frac{\left(42-35f\right)x}{42-35f}=\frac{42-21f}{42-35f}$$

Mā te whakawehe ki te 42-35f ka wetekia te whakareanga ki te 42-35f.

$$x=\frac{42-21f}{42-35f}$$

Whakawehe -21f+42 ki te 42-35f.

$$x=\frac{3\left(2-f\right)}{6-5f}$$

Tē taea kia ōrite te tāupe x ki \frac{3}{5}.

$$x=\frac{3\left(2-f\right)}{6-5f}\text{, }x\neq \frac{3}{5}$$