Whakaoti i te x^2+mx+n/x^2-7x+10=x+1/x-5Rightarrowm+n=?

$$\frac { x ^ { 2 } + m x + n } { x ^ { 2 } - 7 x + 10 } = \frac { x + 1 } { x - 5 } \Rightarrow m + n = ?$$

Whakaoti mō m (complex solution)

$$\left\{\begin{matrix}m=-\frac{x+n+2}{x}\text{, }&x\neq 0\text{ and }x\neq 2\text{ and }x\neq 5\\m\in \mathrm{C}\text{, }&x=0\text{ and }n=-2\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-7x+10,x-5.

$$x^{2}+mx+n=\left(x-2\right)\left(x+1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}+mx+n=x^{2}-x-2$$

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

$$mx+n=x^{2}-x-2-x^{2}$$

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

$$mx+n=-x-2$$

Tangohia te n mai i ngā taha e rua.

$$mx=-x-2-n$$

He hanga arowhānui tō te whārite.

$$xm=-x-n-2$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xm}{x}=\frac{-x-n-2}{x}$$

Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.

$$m=\frac{-x-n-2}{x}$$

Whakawehe -x-2-n ki te x.

$$m=-\frac{x+n+2}{x}$$

Whakaoti mō n (complex solution)

$$n=-\left(mx+x+2\right)$$

$$x\neq 2\text{ and }x\neq 5$$

Ngā Upane Otinga

Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-7x+10,x-5.

$$x^{2}+mx+n=\left(x-2\right)\left(x+1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}+mx+n=x^{2}-x-2$$

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

$$mx+n=x^{2}-x-2-x^{2}$$

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

$$mx+n=-x-2$$

Tangohia te mx mai i ngā taha e rua.

$$n=-x-2-mx$$

Whakaoti mō m

$$\left\{\begin{matrix}m=-\frac{x+n+2}{x}\text{, }&x\neq 0\text{ and }x\neq 5\text{ and }x\neq 2\\m\in \mathrm{R}\text{, }&x=0\text{ and }n=-2\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-7x+10,x-5.

$$x^{2}+mx+n=\left(x-2\right)\left(x+1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}+mx+n=x^{2}-x-2$$

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

$$mx+n=x^{2}-x-2-x^{2}$$

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

$$mx+n=-x-2$$

Tangohia te n mai i ngā taha e rua.

$$mx=-x-2-n$$

He hanga arowhānui tō te whārite.

$$xm=-x-n-2$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xm}{x}=\frac{-x-n-2}{x}$$

Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.

$$m=\frac{-x-n-2}{x}$$

Whakawehe -x-2-n ki te x.

$$m=-\frac{x+n+2}{x}$$

Whakaoti mō n

$$n=-\left(mx+x+2\right)$$

$$x\neq 5\text{ and }x\neq 2$$

Ngā Upane Otinga

Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-7x+10,x-5.

$$x^{2}+mx+n=\left(x-2\right)\left(x+1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}+mx+n=x^{2}-x-2$$

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

$$mx+n=x^{2}-x-2-x^{2}$$

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

$$mx+n=-x-2$$

Tangohia te mx mai i ngā taha e rua.

$$n=-x-2-mx$$