(k-1)x^2+3kx+2k-3=0 eching

$$( k - 1 ) x ^ { 2 } + 3 k x + 2 k - 3 = 0$$

k uchun yechish

$$k=\frac{x^{2}+3}{\left(x+1\right)\left(x+2\right)}$$

$$x\neq -2\text{ and }x\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$kx^{2}-x^{2}+3kx+2k-3=0$$

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

$$kx^{2}+3kx+2k-3=x^{2}$$

3 ni ikki tarafga qo’shing.

$$kx^{2}+3kx+2k=x^{2}+3$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini x^{2}+3x+2 ga bo‘ling.

$$\frac{\left(x^{2}+3x+2\right)k}{x^{2}+3x+2}=\frac{x^{2}+3}{x^{2}+3x+2}$$

x^{2}+3x+2 ga bo'lish x^{2}+3x+2 ga ko'paytirishni bekor qiladi.

$$k=\frac{x^{2}+3}{x^{2}+3x+2}$$

x^{2}+3 ni x^{2}+3x+2 ga bo'lish.

$$k=\frac{x^{2}+3}{\left(x+1\right)\left(x+2\right)}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{k^{2}+20k-12}-3k}{2\left(k-1\right)}\text{; }x=-\frac{\sqrt{k^{2}+20k-12}+3k}{2\left(k-1\right)}\text{, }&k\neq 1\\x=\frac{1}{3}\text{, }&k=1\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{k^{2}+20k-12}-3k}{2\left(k-1\right)}\text{; }x=-\frac{\sqrt{k^{2}+20k-12}+3k}{2\left(k-1\right)}\text{, }&k\leq -4\sqrt{7}-10\text{ or }\left(k\neq 1\text{ and }k\geq 4\sqrt{7}-10\right)\\x=\frac{1}{3}\text{, }&k=1\end{matrix}\right,$$