x+22/(x+4)(x-2)=A/x+4+B/x-2 eching

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

A uchun yechish

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

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(x-2\right)\left(x+4\right) ga, \left(x+4\right)\left(x-2\right),x+4,x-2 ning eng kichik karralisiga ko‘paytiring.

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

x-2 ga A ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x+4 ga B ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

Ikkala tarafdan xB ni ayirish.

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

Ikkala tarafdan 4B ni ayirish.

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

A'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini x-2 ga bo‘ling.

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

x-2 ga bo'lish x-2 ga ko'paytirishni bekor qiladi.

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

B uchun yechish

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

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(x-2\right)\left(x+4\right) ga, \left(x+4\right)\left(x-2\right),x+4,x-2 ning eng kichik karralisiga ko‘paytiring.

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

x-2 ga A ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x+4 ga B ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

Ikkala tarafdan xA ni ayirish.

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

2A ni ikki tarafga qo’shing.

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

B'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini x+4 ga bo‘ling.

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

x+4 ga bo'lish x+4 ga ko'paytirishni bekor qiladi.

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