Whakaoti i te 32y/x^2+16/x=5y

$$\frac { 32 y } { x ^ { 2 } } + \frac { 16 } { x } = 5 y$$

Whakaoti mō y (complex solution)

$$y=-\frac{16x}{32-5x^{2}}$$

$$x\neq -\frac{4\sqrt{10}}{5}\text{ and }x\neq \frac{4\sqrt{10}}{5}\text{ and }x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x^{2},x.

$$32y+x\times 16=5yx^{2}$$

Tangohia te 5yx^{2} mai i ngā taha e rua.

$$32y+x\times 16-5yx^{2}=0$$

Tangohia te x\times 16 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$32y-5yx^{2}=-x\times 16$$

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

$$\left(32-5x^{2}\right)y=-x\times 16$$

He hanga arowhānui tō te whārite.

$$\left(32-5x^{2}\right)y=-16x$$

Whakawehea ngā taha e rua ki te -5x^{2}+32.

$$\frac{\left(32-5x^{2}\right)y}{32-5x^{2}}=-\frac{16x}{32-5x^{2}}$$

Mā te whakawehe ki te -5x^{2}+32 ka wetekia te whakareanga ki te -5x^{2}+32.

$$y=-\frac{16x}{32-5x^{2}}$$

Whakaoti mō y

$$y=-\frac{16x}{32-5x^{2}}$$

$$|x|\neq \frac{4\sqrt{10}}{5}\text{ and }x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x^{2},x.

$$32y+x\times 16=5yx^{2}$$

Tangohia te 5yx^{2} mai i ngā taha e rua.

$$32y+x\times 16-5yx^{2}=0$$

Tangohia te x\times 16 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$32y-5yx^{2}=-x\times 16$$

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

$$\left(32-5x^{2}\right)y=-x\times 16$$

He hanga arowhānui tō te whārite.

$$\left(32-5x^{2}\right)y=-16x$$

Whakawehea ngā taha e rua ki te -5x^{2}+32.

$$\frac{\left(32-5x^{2}\right)y}{32-5x^{2}}=-\frac{16x}{32-5x^{2}}$$

Mā te whakawehe ki te -5x^{2}+32 ka wetekia te whakareanga ki te -5x^{2}+32.

$$y=-\frac{16x}{32-5x^{2}}$$

Whakaoti mō x

$$x=-\frac{4\left(\sqrt{2\left(5y^{2}+2\right)}-2\right)}{5y}$$

$$x=\frac{4\sqrt{2}\left(\sqrt{5y^{2}+2}+\sqrt{2}\right)}{5y}\text{, }y\neq 0$$