k/2x-4-1=x/1-2 eching

$$\frac { k } { 2 x - 4 } - 1 = \frac { x } { 1 - 2 }$$

k uchun yechish

$$k=-2\left(x-2\right)\left(x-1\right)$$

$$x\neq 2$$

Yechim qadamlari

Tenglamaning ikkala tarafini 2\left(x-2\right) ga ko'paytirish.

$$k+2\left(x-2\right)\left(-1\right)=\left(-2x+4\right)x$$

-2 hosil qilish uchun 2 va -1 ni ko'paytirish.

$$k-2\left(x-2\right)=\left(-2x+4\right)x$$

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

$$k-2x+4=\left(-2x+4\right)x$$

-2x+4 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$k-2x+4=-2x^{2}+4x$$

2x ni ikki tarafga qo’shing.

$$k+4=-2x^{2}+4x+2x$$

6x ni olish uchun 4x va 2x ni birlashtirish.

$$k+4=-2x^{2}+6x$$

Ikkala tarafdan 4 ni ayirish.

$$k=-2x^{2}+6x-4$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x=\frac{-\sqrt{1-2k}+3}{2}\text{, }&\text{unconditionally}\\x=\frac{\sqrt{1-2k}+3}{2}\text{, }&k\neq 0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{-\sqrt{1-2k}+3}{2}\text{, }&k\leq \frac{1}{2}\\x=\frac{\sqrt{1-2k}+3}{2}\text{, }&k\neq 0\text{ and }k\leq \frac{1}{2}\end{matrix}\right,$$