3b/2y+3-b-y/x-5=1 eching

$$\frac { 3 b } { 2 y + 3 } - \frac { b - y } { x - 5 } = 1$$

b uchun yechish (complex solution)

$$\left\{\begin{matrix}b=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}\text{, }&y\neq \frac{3x}{2}-9\text{ and }y\neq -\frac{3}{2}\text{ and }x\neq 5\\b\in \mathrm{C}\text{, }&y=3\text{ and }x=8\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(x-5\right)\left(2y+3\right) ga, 2y+3,x-5 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-5\right)\times 3b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

x-5 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(3x-15\right)b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

3x-15 ga b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-15b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

2y+3 ga b-y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-15b-\left(2yb-2y^{2}+3b-3y\right)=\left(x-5\right)\left(2y+3\right)$$

2yb-2y^{2}+3b-3y teskarisini topish uchun har birining teskarisini toping.

$$3xb-15b-2yb+2y^{2}-3b+3y=\left(x-5\right)\left(2y+3\right)$$

-18b ni olish uchun -15b va -3b ni birlashtirish.

$$3xb-18b-2yb+2y^{2}+3y=\left(x-5\right)\left(2y+3\right)$$

x-5 ga 2y+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-18b-2yb+2y^{2}+3y=2xy+3x-10y-15$$

Ikkala tarafdan 2y^{2} ni ayirish.

$$3xb-18b-2yb+3y=2xy+3x-10y-15-2y^{2}$$

Ikkala tarafdan 3y ni ayirish.

$$3xb-18b-2yb=2xy+3x-10y-15-2y^{2}-3y$$

-13y ni olish uchun -10y va -3y ni birlashtirish.

$$3xb-18b-2yb=2xy+3x-13y-15-2y^{2}$$

b'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3x-18-2y\right)b=2xy+3x-13y-15-2y^{2}$$

Tenglama standart shaklda.

$$\left(3x-2y-18\right)b=2xy+3x-2y^{2}-13y-15$$

Ikki tarafini 3x-2y-18 ga bo‘ling.

$$\frac{\left(3x-2y-18\right)b}{3x-2y-18}=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}$$

3x-2y-18 ga bo'lish 3x-2y-18 ga ko'paytirishni bekor qiladi.

$$b=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}$$

b uchun yechish

$$\left\{\begin{matrix}b=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}\text{, }&y\neq \frac{3x}{2}-9\text{ and }y\neq -\frac{3}{2}\text{ and }x\neq 5\\b\in \mathrm{R}\text{, }&y=3\text{ and }x=8\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(x-5\right)\left(2y+3\right) ga, 2y+3,x-5 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-5\right)\times 3b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

x-5 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(3x-15\right)b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

3x-15 ga b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-15b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

2y+3 ga b-y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-15b-\left(2yb-2y^{2}+3b-3y\right)=\left(x-5\right)\left(2y+3\right)$$

2yb-2y^{2}+3b-3y teskarisini topish uchun har birining teskarisini toping.

$$3xb-15b-2yb+2y^{2}-3b+3y=\left(x-5\right)\left(2y+3\right)$$

-18b ni olish uchun -15b va -3b ni birlashtirish.

$$3xb-18b-2yb+2y^{2}+3y=\left(x-5\right)\left(2y+3\right)$$

x-5 ga 2y+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-18b-2yb+2y^{2}+3y=2xy+3x-10y-15$$

Ikkala tarafdan 2y^{2} ni ayirish.

$$3xb-18b-2yb+3y=2xy+3x-10y-15-2y^{2}$$

Ikkala tarafdan 3y ni ayirish.

$$3xb-18b-2yb=2xy+3x-10y-15-2y^{2}-3y$$

-13y ni olish uchun -10y va -3y ni birlashtirish.

$$3xb-18b-2yb=2xy+3x-13y-15-2y^{2}$$

b'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3x-18-2y\right)b=2xy+3x-13y-15-2y^{2}$$

Tenglama standart shaklda.

$$\left(3x-2y-18\right)b=2xy+3x-2y^{2}-13y-15$$

Ikki tarafini 3x-2y-18 ga bo‘ling.

$$\frac{\left(3x-2y-18\right)b}{3x-2y-18}=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}$$

3x-2y-18 ga bo'lish 3x-2y-18 ga ko'paytirishni bekor qiladi.

$$b=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}$$

x uchun yechish

$$\left\{\begin{matrix}x=-\frac{2y^{2}-2by+13y-18b+15}{-2y+3b-3}\text{, }&y\neq -\frac{3}{2}\text{ and }b\neq y\text{ and }b\neq \frac{2y}{3}+1\\x\neq 5\text{, }&y=3\text{ and }b=3\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 5 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-5\right)\left(2y+3\right) ga, 2y+3,x-5 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-5\right)\times 3b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

x-5 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(3x-15\right)b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

3x-15 ga b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-15b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

2y+3 ga b-y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-15b-\left(2yb-2y^{2}+3b-3y\right)=\left(x-5\right)\left(2y+3\right)$$

2yb-2y^{2}+3b-3y teskarisini topish uchun har birining teskarisini toping.

$$3xb-15b-2yb+2y^{2}-3b+3y=\left(x-5\right)\left(2y+3\right)$$

-18b ni olish uchun -15b va -3b ni birlashtirish.

$$3xb-18b-2yb+2y^{2}+3y=\left(x-5\right)\left(2y+3\right)$$

x-5 ga 2y+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xb-18b-2yb+2y^{2}+3y=2xy+3x-10y-15$$

Ikkala tarafdan 2xy ni ayirish.

$$3xb-18b-2yb+2y^{2}+3y-2xy=3x-10y-15$$

Ikkala tarafdan 3x ni ayirish.

$$3xb-18b-2yb+2y^{2}+3y-2xy-3x=-10y-15$$

18b ni ikki tarafga qo’shing.

$$3xb-2yb+2y^{2}+3y-2xy-3x=-10y-15+18b$$

2yb ni ikki tarafga qo’shing.

$$3xb+2y^{2}+3y-2xy-3x=-10y-15+18b+2yb$$

Ikkala tarafdan 2y^{2} ni ayirish.

$$3xb+3y-2xy-3x=-10y-15+18b+2yb-2y^{2}$$

Ikkala tarafdan 3y ni ayirish.

$$3xb-2xy-3x=-10y-15+18b+2yb-2y^{2}-3y$$

-13y ni olish uchun -10y va -3y ni birlashtirish.

$$3xb-2xy-3x=-13y-15+18b+2yb-2y^{2}$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3b-2y-3\right)x=-13y-15+18b+2yb-2y^{2}$$

Tenglama standart shaklda.

$$\left(-2y+3b-3\right)x=-2y^{2}+2by-13y+18b-15$$

Ikki tarafini -2y+3b-3 ga bo‘ling.

$$\frac{\left(-2y+3b-3\right)x}{-2y+3b-3}=\frac{-2y^{2}+2by-13y+18b-15}{-2y+3b-3}$$

-2y+3b-3 ga bo'lish -2y+3b-3 ga ko'paytirishni bekor qiladi.

$$x=\frac{-2y^{2}+2by-13y+18b-15}{-2y+3b-3}$$

x qiymati 5 teng bo‘lmaydi.

$$x=\frac{-2y^{2}+2by-13y+18b-15}{-2y+3b-3}\text{, }x\neq 5$$