3/x+(6x+5)-6x+1/3x-1=3x+9x+6/3x-1+3x^2+1/x eching

$$\frac { 3 } { x } + ( 6 x + 5 ) - \frac { 6 x + 1 } { 3 x - 1 } = 3 x + \frac { 9 x + 6 } { 3 x - 1 } + \frac { 3 x ^ { 2 } + 1 } { x }$$

x uchun yechish

$$x=-\frac{1}{3}\approx -0,333333333$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 0,\frac{1}{3} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(3x-1\right) ga, x,3x-1 ning eng kichik karralisiga ko‘paytiring.

$$\left(3x-1\right)\times 3+6xx\left(3x-1\right)+x\left(3x-1\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

3x-1 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x-3+6xx\left(3x-1\right)+x\left(3x-1\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

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

$$9x-3+6x^{2}\left(3x-1\right)+x\left(3x-1\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

6x^{2} ga 3x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x-3+18x^{3}-6x^{2}+x\left(3x-1\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

x ga 3x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x-3+18x^{3}-6x^{2}+\left(3x^{2}-x\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

3x^{2}-x ga 5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x-3+18x^{3}-6x^{2}+15x^{2}-5x-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

9x^{2} ni olish uchun -6x^{2} va 15x^{2} ni birlashtirish.

$$9x-3+18x^{3}+9x^{2}-5x-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

4x ni olish uchun 9x va -5x ni birlashtirish.

$$4x-3+18x^{3}+9x^{2}-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

x ga 6x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x-3+18x^{3}+9x^{2}-\left(6x^{2}+x\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

6x^{2}+x teskarisini topish uchun har birining teskarisini toping.

$$4x-3+18x^{3}+9x^{2}-6x^{2}-x=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

3x^{2} ni olish uchun 9x^{2} va -6x^{2} ni birlashtirish.

$$4x-3+18x^{3}+3x^{2}-x=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

3x ni olish uchun 4x va -x ni birlashtirish.

$$3x-3+18x^{3}+3x^{2}=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

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

$$3x-3+18x^{3}+3x^{2}=3x^{2}\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

3x^{2} ga 3x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-3+18x^{3}+3x^{2}=9x^{3}-3x^{2}+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

x ga 9x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-3+18x^{3}+3x^{2}=9x^{3}-3x^{2}+9x^{2}+6x+\left(3x-1\right)\left(3x^{2}+1\right)$$

6x^{2} ni olish uchun -3x^{2} va 9x^{2} ni birlashtirish.

$$3x-3+18x^{3}+3x^{2}=9x^{3}+6x^{2}+6x+\left(3x-1\right)\left(3x^{2}+1\right)$$

3x-1 ga 3x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-3+18x^{3}+3x^{2}=9x^{3}+6x^{2}+6x+9x^{3}+3x-3x^{2}-1$$

18x^{3} ni olish uchun 9x^{3} va 9x^{3} ni birlashtirish.

$$3x-3+18x^{3}+3x^{2}=18x^{3}+6x^{2}+6x+3x-3x^{2}-1$$

9x ni olish uchun 6x va 3x ni birlashtirish.

$$3x-3+18x^{3}+3x^{2}=18x^{3}+6x^{2}+9x-3x^{2}-1$$

3x^{2} ni olish uchun 6x^{2} va -3x^{2} ni birlashtirish.

$$3x-3+18x^{3}+3x^{2}=18x^{3}+3x^{2}+9x-1$$

Ikkala tarafdan 18x^{3} ni ayirish.

$$3x-3+18x^{3}+3x^{2}-18x^{3}=3x^{2}+9x-1$$

0 ni olish uchun 18x^{3} va -18x^{3} ni birlashtirish.

$$3x-3+3x^{2}=3x^{2}+9x-1$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$3x-3+3x^{2}-3x^{2}=9x-1$$

0 ni olish uchun 3x^{2} va -3x^{2} ni birlashtirish.

$$3x-3=9x-1$$

Ikkala tarafdan 9x ni ayirish.

$$3x-3-9x=-1$$

-6x ni olish uchun 3x va -9x ni birlashtirish.

$$-6x-3=-1$$

3 ni ikki tarafga qo’shing.

$$-6x=-1+3$$

2 olish uchun -1 va 3'ni qo'shing.

$$-6x=2$$

Ikki tarafini -6 ga bo‘ling.

$$x=\frac{2}{-6}$$

\frac{2}{-6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{3}$$