Whakaoti i te operatorname{lon}x-3/5=x+1/3-2

$$\operatorname { lon } \frac { x - 3 } { 5 } = \frac { x + 1 } { 3 } - 2$$

Whakaoti mō l (complex solution)

$$\left\{\begin{matrix}l=-\frac{5\left(5-x\right)}{3no\left(x-3\right)}\text{, }&n\neq 0\text{ and }o\neq 0\text{ and }x\neq 3\\l\in \mathrm{C}\text{, }&\left(o=0\text{ or }n=0\right)\text{ and }x=5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 15, arā, te tauraro pātahi he tino iti rawa te kitea o 5,3.

$$3lon\left(x-3\right)=5\left(x+1\right)-30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3lon ki te x-3.

$$3lonx-9lon=5\left(x+1\right)-30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x+1.

$$3lonx-9lon=5x+5-30$$

Tangohia te 30 i te 5, ka -25.

$$3lonx-9lon=5x-25$$

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

$$\left(3onx-9on\right)l=5x-25$$

He hanga arowhānui tō te whārite.

$$\left(3nox-9no\right)l=5x-25$$

Whakawehea ngā taha e rua ki te 3nxo-9on.

$$\frac{\left(3nox-9no\right)l}{3nox-9no}=\frac{5x-25}{3nox-9no}$$

Mā te whakawehe ki te 3nxo-9on ka wetekia te whakareanga ki te 3nxo-9on.

$$l=\frac{5x-25}{3nox-9no}$$

Whakawehe -25+5x ki te 3nxo-9on.

$$l=\frac{5\left(x-5\right)}{3no\left(x-3\right)}$$

Whakaoti mō n (complex solution)

$$\left\{\begin{matrix}n=-\frac{5\left(5-x\right)}{3lo\left(x-3\right)}\text{, }&l\neq 0\text{ and }o\neq 0\text{ and }x\neq 3\\n\in \mathrm{C}\text{, }&\left(o=0\text{ or }l=0\right)\text{ and }x=5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 15, arā, te tauraro pātahi he tino iti rawa te kitea o 5,3.

$$3lon\left(x-3\right)=5\left(x+1\right)-30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3lon ki te x-3.

$$3lonx-9lno=5\left(x+1\right)-30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x+1.

$$3lonx-9lno=5x+5-30$$

Tangohia te 30 i te 5, ka -25.

$$3lonx-9lno=5x-25$$

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

$$\left(3lox-9lo\right)n=5x-25$$

Whakawehea ngā taha e rua ki te 3lxo-9ol.

$$\frac{\left(3lox-9lo\right)n}{3lox-9lo}=\frac{5x-25}{3lox-9lo}$$

Mā te whakawehe ki te 3lxo-9ol ka wetekia te whakareanga ki te 3lxo-9ol.

$$n=\frac{5x-25}{3lox-9lo}$$

Whakawehe -25+5x ki te 3lxo-9ol.

$$n=\frac{5\left(x-5\right)}{3lo\left(x-3\right)}$$

Whakaoti mō l

$$\left\{\begin{matrix}l=-\frac{5\left(5-x\right)}{3no\left(x-3\right)}\text{, }&n\neq 0\text{ and }o\neq 0\text{ and }x\neq 3\\l\in \mathrm{R}\text{, }&\left(o=0\text{ or }n=0\right)\text{ and }x=5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 15, arā, te tauraro pātahi he tino iti rawa te kitea o 5,3.

$$3lon\left(x-3\right)=5\left(x+1\right)-30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3lon ki te x-3.

$$3lonx-9lon=5\left(x+1\right)-30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x+1.

$$3lonx-9lon=5x+5-30$$

Tangohia te 30 i te 5, ka -25.

$$3lonx-9lon=5x-25$$

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

$$\left(3onx-9on\right)l=5x-25$$

He hanga arowhānui tō te whārite.

$$\left(3nox-9no\right)l=5x-25$$

Whakawehea ngā taha e rua ki te 3nxo-9on.

$$\frac{\left(3nox-9no\right)l}{3nox-9no}=\frac{5x-25}{3nox-9no}$$

Mā te whakawehe ki te 3nxo-9on ka wetekia te whakareanga ki te 3nxo-9on.

$$l=\frac{5x-25}{3nox-9no}$$

Whakawehe -25+5x ki te 3nxo-9on.

$$l=\frac{5\left(x-5\right)}{3no\left(x-3\right)}$$

Whakaoti mō n

$$\left\{\begin{matrix}n=-\frac{5\left(5-x\right)}{3lo\left(x-3\right)}\text{, }&l\neq 0\text{ and }o\neq 0\text{ and }x\neq 3\\n\in \mathrm{R}\text{, }&\left(o=0\text{ or }l=0\right)\text{ and }x=5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 15, arā, te tauraro pātahi he tino iti rawa te kitea o 5,3.

$$3lon\left(x-3\right)=5\left(x+1\right)-30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3lon ki te x-3.

$$3lonx-9lno=5\left(x+1\right)-30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x+1.

$$3lonx-9lno=5x+5-30$$

Tangohia te 30 i te 5, ka -25.

$$3lonx-9lno=5x-25$$

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

$$\left(3lox-9lo\right)n=5x-25$$

Whakawehea ngā taha e rua ki te 3lxo-9ol.

$$\frac{\left(3lox-9lo\right)n}{3lox-9lo}=\frac{5x-25}{3lox-9lo}$$

Mā te whakawehe ki te 3lxo-9ol ka wetekia te whakareanga ki te 3lxo-9ol.

$$n=\frac{5x-25}{3lox-9lo}$$

Whakawehe -25+5x ki te 3lxo-9ol.

$$n=\frac{5\left(x-5\right)}{3lo\left(x-3\right)}$$