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

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

b uchun yechish

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

$$x\neq 18\text{ and }x\neq -\frac{3}{2}\text{ and }x\neq 5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

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

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

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

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

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

2xb-2x^{2}+3b-3x teskarisini topish uchun har birining teskarisini toping.

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

xb ni olish uchun 3xb va -2xb ni birlashtirish.

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

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

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

x-5 ga 2x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$xb-18b+2x^{2}+3x=2x^{2}-7x-15$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$xb-18b+3x=2x^{2}-7x-15-2x^{2}$$

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

$$xb-18b+3x=-7x-15$$

Ikkala tarafdan 3x ni ayirish.

$$xb-18b=-7x-15-3x$$

-10x ni olish uchun -7x va -3x ni birlashtirish.

$$xb-18b=-10x-15$$

b'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x-18\right)b=-10x-15$$

Ikki tarafini x-18 ga bo‘ling.

$$\frac{\left(x-18\right)b}{x-18}=\frac{-10x-15}{x-18}$$

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

$$b=\frac{-10x-15}{x-18}$$

-10x-15 ni x-18 ga bo'lish.

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

x uchun yechish

$$x=-\frac{3\left(5-6b\right)}{b+10}$$

$$b\neq 0\text{ and }b\neq -10\text{ and }b\neq 5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

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

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

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

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

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

2xb-2x^{2}+3b-3x teskarisini topish uchun har birining teskarisini toping.

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

xb ni olish uchun 3xb va -2xb ni birlashtirish.

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

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

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

x-5 ga 2x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$xb-18b+2x^{2}+3x=2x^{2}-7x-15$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$xb-18b+2x^{2}+3x-2x^{2}=-7x-15$$

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

$$xb-18b+3x=-7x-15$$

7x ni ikki tarafga qo’shing.

$$xb-18b+3x+7x=-15$$

10x ni olish uchun 3x va 7x ni birlashtirish.

$$xb-18b+10x=-15$$

18b ni ikki tarafga qo’shing.

$$xb+10x=-15+18b$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(b+10\right)x=-15+18b$$

Tenglama standart shaklda.

$$\left(b+10\right)x=18b-15$$

Ikki tarafini b+10 ga bo‘ling.

$$\frac{\left(b+10\right)x}{b+10}=\frac{18b-15}{b+10}$$

b+10 ga bo'lish b+10 ga ko'paytirishni bekor qiladi.

$$x=\frac{18b-15}{b+10}$$

-15+18b ni b+10 ga bo'lish.

$$x=\frac{3\left(6b-5\right)}{b+10}$$

x qiymati -\frac{3}{2},5 qiymatlaridan birortasiga teng bo‘lmaydi.

$$x=\frac{3\left(6b-5\right)}{b+10}\text{, }x\neq -\frac{3}{2}\text{ and }x\neq 5$$