Whakaoti i te f(x)=x^2+5x+6quadyquadg(x)=x^2-3x-10

$$f ( x ) = x ^ { 2 } + 5 x + 6 \quad y \quad g ( x ) = x ^ { 2 } - 3 x - 10$$

Whakaoti mō g (complex solution)

$$\left\{\begin{matrix}g=-\frac{4x+5}{3xy}\text{, }&y\neq 0\text{ and }x\neq 0\\g\in \mathrm{C}\text{, }&x=-\frac{5}{4}\text{ and }y=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$5x+6ygx=x^{2}-3x-10-x^{2}$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$5x+6ygx=-3x-10$$

Tangohia te 5x mai i ngā taha e rua.

$$6ygx=-3x-10-5x$$

Pahekotia te -3x me -5x, ka -8x.

$$6ygx=-8x-10$$

He hanga arowhānui tō te whārite.

$$6xyg=-8x-10$$

Whakawehea ngā taha e rua ki te 6yx.

$$\frac{6xyg}{6xy}=\frac{-8x-10}{6xy}$$

Mā te whakawehe ki te 6yx ka wetekia te whakareanga ki te 6yx.

$$g=\frac{-8x-10}{6xy}$$

Whakawehe -10-8x ki te 6yx.

$$g=-\frac{4x+5}{3xy}$$

Whakaoti mō g

$$\left\{\begin{matrix}g=-\frac{4x+5}{3xy}\text{, }&y\neq 0\text{ and }x\neq 0\\g\in \mathrm{R}\text{, }&x=-\frac{5}{4}\text{ and }y=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$5x+6ygx=x^{2}-3x-10-x^{2}$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$5x+6ygx=-3x-10$$

Tangohia te 5x mai i ngā taha e rua.

$$6ygx=-3x-10-5x$$

Pahekotia te -3x me -5x, ka -8x.

$$6ygx=-8x-10$$

He hanga arowhānui tō te whārite.

$$6xyg=-8x-10$$

Whakawehea ngā taha e rua ki te 6yx.

$$\frac{6xyg}{6xy}=\frac{-8x-10}{6xy}$$

Mā te whakawehe ki te 6yx ka wetekia te whakareanga ki te 6yx.

$$g=\frac{-8x-10}{6xy}$$

Whakawehe -8x-10 ki te 6yx.

$$g=-\frac{4x+5}{3xy}$$

Whakaoti mō x

$$x=-\frac{5}{3gy+4}$$

$$g=0\text{ or }y\neq -\frac{4}{3g}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x^{2}+5x+6ygx-x^{2}=-3x-10$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$5x+6ygx=-3x-10$$

Me tāpiri te 3x ki ngā taha e rua.

$$5x+6ygx+3x=-10$$

Pahekotia te 5x me 3x, ka 8x.

$$8x+6ygx=-10$$

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

$$\left(8+6yg\right)x=-10$$

He hanga arowhānui tō te whārite.

$$\left(6gy+8\right)x=-10$$

Whakawehea ngā taha e rua ki te 6gy+8.

$$\frac{\left(6gy+8\right)x}{6gy+8}=-\frac{10}{6gy+8}$$

Mā te whakawehe ki te 6gy+8 ka wetekia te whakareanga ki te 6gy+8.

$$x=-\frac{10}{6gy+8}$$

Whakawehe -10 ki te 6gy+8.

$$x=-\frac{5}{3gy+4}$$