(a-1)x^2-2ax+a+1=0 eching

$$( a - 1 ) x ^ { 2 } - 2 a x + a + 1 = 0$$

a uchun yechish (complex solution)

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

a-1 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$ax^{2}-x^{2}-2ax+a+1=0$$

x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$ax^{2}-2ax+a+1=x^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$ax^{2}-2ax+a=x^{2}-1$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-2x+1\right)a=x^{2}-1$$

Ikki tarafini x^{2}-2x+1 ga bo‘ling.

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

x^{2}-2x+1 ga bo'lish x^{2}-2x+1 ga ko'paytirishni bekor qiladi.

$$a=\frac{x^{2}-1}{x^{2}-2x+1}$$

x^{2}-1 ni x^{2}-2x+1 ga bo'lish.

$$a=\frac{x+1}{x-1}$$

a uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

a-1 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$ax^{2}-x^{2}-2ax+a+1=0$$

x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$ax^{2}-2ax+a+1=x^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$ax^{2}-2ax+a=x^{2}-1$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-2x+1\right)a=x^{2}-1$$

Ikki tarafini x^{2}-2x+1 ga bo‘ling.

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

x^{2}-2x+1 ga bo'lish x^{2}-2x+1 ga ko'paytirishni bekor qiladi.

$$a=\frac{x^{2}-1}{x^{2}-2x+1}$$

x^{2}-1 ni x^{2}-2x+1 ga bo'lish.

$$a=\frac{x+1}{x-1}$$

x uchun yechish

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