x+1/y-1=x/y-1 eching

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

x uchun yechish

$$x=-y^{2}$$

$$y\neq 1\text{ and }y\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini y\left(y-1\right) ga, y-1,y ning eng kichik karralisiga ko‘paytiring.

$$y\left(x+1\right)=\left(y-1\right)x+y\left(y-1\right)\left(-1\right)$$

y ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$yx+y=\left(y-1\right)x+y\left(y-1\right)\left(-1\right)$$

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

$$yx+y=yx-x+y\left(y-1\right)\left(-1\right)$$

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

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

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

$$yx+y=yx-x-y^{2}+y$$

Ikkala tarafdan yx ni ayirish.

$$yx+y-yx=-x-y^{2}+y$$

0 ni olish uchun yx va -yx ni birlashtirish.

$$y=-x-y^{2}+y$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-x-y^{2}+y=y$$

y^{2} ni ikki tarafga qo’shing.

$$-x+y=y+y^{2}$$

Ikkala tarafdan y ni ayirish.

$$-x=y+y^{2}-y$$

0 ni olish uchun y va -y ni birlashtirish.

$$-x=y^{2}$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x}{-1}=\frac{y^{2}}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x=\frac{y^{2}}{-1}$$

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

$$x=-y^{2}$$

y uchun yechish (complex solution)

$$\left\{\begin{matrix}y=i\sqrt{x}\text{, }&x\neq 0\\y=-i\sqrt{x}\text{, }&x\neq -1\text{ and }x\neq 0\end{matrix}\right,$$

y uchun yechish

$$\left\{\begin{matrix}y=-\sqrt{-x}\text{, }&x<0\\y=\sqrt{-x}\text{, }&x\neq -1\text{ and }x<0\end{matrix}\right,$$