3x^{2}+5x+7+2x^3+3x+16/x^2+x=10x^3+12x+4/x-2+7x^3/x+1 eching

$$3 x ^ { 2 } + 5 x + 7 + \frac { 2 x ^ { 3 } + 3 x + 16 } { x ^ { 2 } + x } = \frac { 10 x ^ { 3 } + 12 x + 4 } { x } - \frac { 2 + 7 x ^ { 3 } } { x + 1 }$$

x uchun yechish

$$x=3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -1,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x+1\right) ga, x^{2}+x,x,x+1 ning eng kichik karralisiga ko‘paytiring.

$$3x^{2}x\left(x+1\right)+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$3x^{3}\left(x+1\right)+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

3x^{3} ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{4}+3x^{3}+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$3x^{4}+3x^{3}+5x^{2}\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

5x^{2} ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{4}+3x^{3}+5x^{3}+5x^{2}+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

8x^{3} ni olish uchun 3x^{3} va 5x^{3} ni birlashtirish.

$$3x^{4}+8x^{3}+5x^{2}+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

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

$$3x^{4}+8x^{3}+5x^{2}+\left(x^{2}+x\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

x^{2}+x ga 7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{4}+8x^{3}+5x^{2}+7x^{2}+7x+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

12x^{2} ni olish uchun 5x^{2} va 7x^{2} ni birlashtirish.

$$3x^{4}+8x^{3}+12x^{2}+7x+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

10x^{3} ni olish uchun 8x^{3} va 2x^{3} ni birlashtirish.

$$3x^{4}+10x^{3}+12x^{2}+7x+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

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

$$3x^{4}+10x^{3}+12x^{2}+10x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

x+1 ga 10x^{3}+12x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-x\left(2+7x^{3}\right)$$

x ga 2+7x^{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-\left(2x+7x^{4}\right)$$

2x+7x^{4} teskarisini topish uchun har birining teskarisini toping.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-2x-7x^{4}$$

14x ni olish uchun 16x va -2x ni birlashtirish.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+14x+10x^{3}+4-7x^{4}$$

3x^{4} ni olish uchun 10x^{4} va -7x^{4} ni birlashtirish.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=3x^{4}+12x^{2}+14x+10x^{3}+4$$

Ikkala tarafdan 3x^{4} ni ayirish.

$$3x^{4}+10x^{3}+12x^{2}+10x+16-3x^{4}=12x^{2}+14x+10x^{3}+4$$

0 ni olish uchun 3x^{4} va -3x^{4} ni birlashtirish.

$$10x^{3}+12x^{2}+10x+16=12x^{2}+14x+10x^{3}+4$$

Ikkala tarafdan 12x^{2} ni ayirish.

$$10x^{3}+12x^{2}+10x+16-12x^{2}=14x+10x^{3}+4$$

0 ni olish uchun 12x^{2} va -12x^{2} ni birlashtirish.

$$10x^{3}+10x+16=14x+10x^{3}+4$$

Ikkala tarafdan 14x ni ayirish.

$$10x^{3}+10x+16-14x=10x^{3}+4$$

-4x ni olish uchun 10x va -14x ni birlashtirish.

$$10x^{3}-4x+16=10x^{3}+4$$

Ikkala tarafdan 10x^{3} ni ayirish.

$$10x^{3}-4x+16-10x^{3}=4$$

0 ni olish uchun 10x^{3} va -10x^{3} ni birlashtirish.

$$-4x+16=4$$

Ikkala tarafdan 16 ni ayirish.

$$-4x=4-16$$

-12 olish uchun 4 dan 16 ni ayirish.

$$-4x=-12$$

Ikki tarafini -4 ga bo‘ling.

$$x=\frac{-12}{-4}$$

3 ni olish uchun -12 ni -4 ga bo‘ling.

$$x=3$$