Whakaoti i te x+22/(x+4)(x-2)=A/x+4+B/x-2

$$\frac { x + 22 } { ( x + 4 ) ( x - 2 ) } = \frac { A } { x + 4 } + \frac { B } { x - 2 }$$

Whakaoti mō A

$$A=-\frac{22-4B+x-Bx}{2-x}$$

$$x\neq -4\text{ and }x\neq 2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o \left(x+4\right)\left(x-2\right),x+4,x-2.

$$x+22=\left(x-2\right)A+\left(x+4\right)B$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te A.

$$x+22=xA-2A+\left(x+4\right)B$$

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

$$x+22=xA-2A+xB+4B$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$xA-2A+xB+4B=x+22$$

Tangohia te xB mai i ngā taha e rua.

$$xA-2A+4B=x+22-xB$$

Tangohia te 4B mai i ngā taha e rua.

$$xA-2A=x+22-xB-4B$$

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

$$\left(x-2\right)A=x+22-xB-4B$$

He hanga arowhānui tō te whārite.

$$\left(x-2\right)A=22-4B+x-Bx$$

Whakawehea ngā taha e rua ki te x-2.

$$\frac{\left(x-2\right)A}{x-2}=\frac{22-4B+x-Bx}{x-2}$$

Mā te whakawehe ki te x-2 ka wetekia te whakareanga ki te x-2.

$$A=\frac{22-4B+x-Bx}{x-2}$$

Whakaoti mō B

$$B=\frac{22+2A+x-Ax}{x+4}$$

$$x\neq -4\text{ and }x\neq 2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o \left(x+4\right)\left(x-2\right),x+4,x-2.

$$x+22=\left(x-2\right)A+\left(x+4\right)B$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te A.

$$x+22=xA-2A+\left(x+4\right)B$$

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

$$x+22=xA-2A+xB+4B$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$xA-2A+xB+4B=x+22$$

Tangohia te xA mai i ngā taha e rua.

$$-2A+xB+4B=x+22-xA$$

Me tāpiri te 2A ki ngā taha e rua.

$$xB+4B=x+22-xA+2A$$

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

$$\left(x+4\right)B=x+22-xA+2A$$

He hanga arowhānui tō te whārite.

$$\left(x+4\right)B=22+2A+x-Ax$$

Whakawehea ngā taha e rua ki te x+4.

$$\frac{\left(x+4\right)B}{x+4}=\frac{22+2A+x-Ax}{x+4}$$

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

$$B=\frac{22+2A+x-Ax}{x+4}$$