Whakaoti i te x+4/x=z/z+4

$$\frac { x + 4 } { x } = \frac { z } { z + 4 }$$

Whakaoti mō x

$$x=-\left(z+4\right)$$

$$z\neq -4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(z+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,z+4.

$$\left(z+4\right)\left(x+4\right)=xz$$

Whakamahia te āhuatanga tohatoha hei whakarea te z+4 ki te x+4.

$$zx+4z+4x+16=xz$$

Tangohia te xz mai i ngā taha e rua.

$$zx+4z+4x+16-xz=0$$

Pahekotia te zx me -xz, ka 0.

$$4z+4x+16=0$$

Tangohia te 4z mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$4x+16=-4z$$

Tangohia te 16 mai i ngā taha e rua.

$$4x=-4z-16$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x}{4}=\frac{-4z-16}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x=\frac{-4z-16}{4}$$

Whakawehe -4z-16 ki te 4.

$$x=-z-4$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-z-4\text{, }x\neq 0$$

Whakaoti mō z

$$z=-\left(x+4\right)$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe z ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(z+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,z+4.

$$\left(z+4\right)\left(x+4\right)=xz$$

Whakamahia te āhuatanga tohatoha hei whakarea te z+4 ki te x+4.

$$zx+4z+4x+16=xz$$

Tangohia te xz mai i ngā taha e rua.

$$zx+4z+4x+16-xz=0$$

Pahekotia te zx me -xz, ka 0.

$$4z+4x+16=0$$

Tangohia te 4x mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$4z+16=-4x$$

Tangohia te 16 mai i ngā taha e rua.

$$4z=-4x-16$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4z}{4}=\frac{-4x-16}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$z=\frac{-4x-16}{4}$$

Whakawehe -4x-16 ki te 4.

$$z=-x-4$$

Tē taea kia ōrite te tāupe z ki -4.

$$z=-x-4\text{, }z\neq -4$$