(x-1)*P(x)=x^2-3x+2 eching

$$( x - 1 ) \cdot P ( x ) = x ^ { 2 } - 3 x + 2$$

P uchun yechish (complex solution)

$$\left\{\begin{matrix}P=\frac{x-2}{x}\text{, }&x\neq 0\\P\in \mathrm{C}\text{, }&x=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x-1 ga P ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(xP-P\right)x=x^{2}-3x+2$$

xP-P ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Px^{2}-Px=x^{2}-3x+2$$

P'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-x\right)P=x^{2}-3x+2$$

Ikki tarafini x^{2}-x ga bo‘ling.

$$\frac{\left(x^{2}-x\right)P}{x^{2}-x}=\frac{\left(x-2\right)\left(x-1\right)}{x^{2}-x}$$

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

$$P=\frac{\left(x-2\right)\left(x-1\right)}{x^{2}-x}$$

\left(-2+x\right)\left(-1+x\right) ni x^{2}-x ga bo'lish.

$$P=\frac{x-2}{x}$$

P uchun yechish

$$\left\{\begin{matrix}P=\frac{x-2}{x}\text{, }&x\neq 0\\P\in \mathrm{R}\text{, }&x=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x-1 ga P ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(xP-P\right)x=x^{2}-3x+2$$

xP-P ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Px^{2}-Px=x^{2}-3x+2$$

P'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-x\right)P=x^{2}-3x+2$$

Ikki tarafini x^{2}-x ga bo‘ling.

$$\frac{\left(x^{2}-x\right)P}{x^{2}-x}=\frac{\left(x-2\right)\left(x-1\right)}{x^{2}-x}$$

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

$$P=\frac{\left(x-2\right)\left(x-1\right)}{x^{2}-x}$$

\left(-2+x\right)\left(-1+x\right) ni x^{2}-x ga bo'lish.

$$P=\frac{x-2}{x}$$

x uchun yechish

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=-\frac{2}{P-1}\text{, }&P\neq 1\end{matrix}\right,$$