y(x+y)-x=y(y+1)+1 eching

$$y(x+y)-x=y(y+1)+1$$

x uchun yechish

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

$$y\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

$$yx+y^{2}-x=y^{2}+y+1$$

Ikkala tarafdan y^{2} ni ayirish.

$$yx-x=y^{2}+y+1-y^{2}$$

0 ni olish uchun y^{2} va -y^{2} ni birlashtirish.

$$yx-x=y+1$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini y-1 ga bo‘ling.

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

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

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

y uchun yechish

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

$$x\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

$$yx+y^{2}-x=y^{2}+y+1$$

Ikkala tarafdan y^{2} ni ayirish.

$$yx+y^{2}-x-y^{2}=y+1$$

0 ni olish uchun y^{2} va -y^{2} ni birlashtirish.

$$yx-x=y+1$$

Ikkala tarafdan y ni ayirish.

$$yx-x-y=1$$

x ni ikki tarafga qo’shing.

$$yx-y=1+x$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini x-1 ga bo‘ling.

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

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

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