Whakaoti i te 36/4x-2+8x=12y-3/5

$$\frac { 36 } { 4 x - 2 } + 8 x = \frac { 12 y - 3 } { 5 }$$

Whakaoti mō y

$$y=-\frac{80x^{2}-34x+87}{12\left(1-2x\right)}$$

$$x\neq \frac{1}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 10\left(2x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 4x-2,5.

$$5\times 36+8x\times 10\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

Whakareatia te 5 ki te 36, ka 180.

$$180+8x\times 10\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

Whakareatia te 8 ki te 10, ka 80.

$$180+80x\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 80x ki te 2x-1.

$$180+160x^{2}-80x=\left(4x-2\right)\left(12y-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-2 ki te 12y-3.

$$180+160x^{2}-80x=48xy-12x-24y+6$$

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

$$48xy-12x-24y+6=180+160x^{2}-80x$$

Me tāpiri te 12x ki ngā taha e rua.

$$48xy-24y+6=180+160x^{2}-80x+12x$$

Pahekotia te -80x me 12x, ka -68x.

$$48xy-24y+6=180+160x^{2}-68x$$

Tangohia te 6 mai i ngā taha e rua.

$$48xy-24y=180+160x^{2}-68x-6$$

Tangohia te 6 i te 180, ka 174.

$$48xy-24y=174+160x^{2}-68x$$

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

$$\left(48x-24\right)y=174+160x^{2}-68x$$

He hanga arowhānui tō te whārite.

$$\left(48x-24\right)y=160x^{2}-68x+174$$

Whakawehea ngā taha e rua ki te 48x-24.

$$\frac{\left(48x-24\right)y}{48x-24}=\frac{160x^{2}-68x+174}{48x-24}$$

Mā te whakawehe ki te 48x-24 ka wetekia te whakareanga ki te 48x-24.

$$y=\frac{160x^{2}-68x+174}{48x-24}$$

Whakawehe 174+160x^{2}-68x ki te 48x-24.

$$y=\frac{80x^{2}-34x+87}{12\left(2x-1\right)}$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

$$x=-\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

Whakaoti mō x

$$x=\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

$$x=-\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}\text{, }y\geq 5\sqrt{2}+\frac{23}{12}\text{ or }y\leq \frac{23}{12}-5\sqrt{2}$$