x+1/x-1+x+2/x-2=22x+30/11x-18 eching

$$\frac { x + 1 } { x - 1 } + \frac { x + 2 } { x - 2 } = \frac { 22 x + 30 } { 11 x - 18 }$$

x uchun yechish

$$x=-6$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 1,\frac{18}{11},2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-2\right)\left(x-1\right)\left(11x-18\right) ga, x-1,x-2,11x-18 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-2\right)\left(11x-18\right)\left(x+1\right)+\left(x-1\right)\left(11x-18\right)\left(x+2\right)=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

x-2 ga 11x-18 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(11x^{2}-40x+36\right)\left(x+1\right)+\left(x-1\right)\left(11x-18\right)\left(x+2\right)=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

11x^{2}-40x+36 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$11x^{3}-29x^{2}-4x+36+\left(x-1\right)\left(11x-18\right)\left(x+2\right)=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

x-1 ga 11x-18 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$11x^{3}-29x^{2}-4x+36+\left(11x^{2}-29x+18\right)\left(x+2\right)=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

11x^{2}-29x+18 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$11x^{3}-29x^{2}-4x+36+11x^{3}-7x^{2}-40x+36=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

22x^{3} ni olish uchun 11x^{3} va 11x^{3} ni birlashtirish.

$$22x^{3}-29x^{2}-4x+36-7x^{2}-40x+36=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

-36x^{2} ni olish uchun -29x^{2} va -7x^{2} ni birlashtirish.

$$22x^{3}-36x^{2}-4x+36-40x+36=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

-44x ni olish uchun -4x va -40x ni birlashtirish.

$$22x^{3}-36x^{2}-44x+36+36=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

72 olish uchun 36 va 36'ni qo'shing.

$$22x^{3}-36x^{2}-44x+72=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

x-2 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$22x^{3}-36x^{2}-44x+72=\left(x^{2}-3x+2\right)\left(22x+30\right)$$

x^{2}-3x+2 ga 22x+30 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$22x^{3}-36x^{2}-44x+72=22x^{3}-36x^{2}-46x+60$$

Ikkala tarafdan 22x^{3} ni ayirish.

$$22x^{3}-36x^{2}-44x+72-22x^{3}=-36x^{2}-46x+60$$

0 ni olish uchun 22x^{3} va -22x^{3} ni birlashtirish.

$$-36x^{2}-44x+72=-36x^{2}-46x+60$$

36x^{2} ni ikki tarafga qo’shing.

$$-36x^{2}-44x+72+36x^{2}=-46x+60$$

0 ni olish uchun -36x^{2} va 36x^{2} ni birlashtirish.

$$-44x+72=-46x+60$$

46x ni ikki tarafga qo’shing.

$$-44x+72+46x=60$$

2x ni olish uchun -44x va 46x ni birlashtirish.

$$2x+72=60$$

Ikkala tarafdan 72 ni ayirish.

$$2x=60-72$$

-12 olish uchun 60 dan 72 ni ayirish.

$$2x=-12$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{-12}{2}$$

-6 ni olish uchun -12 ni 2 ga bo‘ling.

$$x=-6$$