3/2x-2+5/x+1=4/x-1 eching

$$\frac { 3 } { 2 x - 2 } + \frac { 5 } { x + 1 } = \frac { 4 } { x - 1 }$$

x uchun yechish

$$x=3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$\left(x+1\right)\times 3+\left(2x-2\right)\times 5=\left(2x+2\right)\times 4$$

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

$$3x+3+\left(2x-2\right)\times 5=\left(2x+2\right)\times 4$$

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

$$3x+3+10x-10=\left(2x+2\right)\times 4$$

13x ni olish uchun 3x va 10x ni birlashtirish.

$$13x+3-10=\left(2x+2\right)\times 4$$

-7 olish uchun 3 dan 10 ni ayirish.

$$13x-7=\left(2x+2\right)\times 4$$

2x+2 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$13x-7=8x+8$$

Ikkala tarafdan 8x ni ayirish.

$$13x-7-8x=8$$

5x ni olish uchun 13x va -8x ni birlashtirish.

$$5x-7=8$$

7 ni ikki tarafga qo’shing.

$$5x=8+7$$

15 olish uchun 8 va 7'ni qo'shing.

$$5x=15$$

Ikki tarafini 5 ga bo‘ling.

$$x=\frac{15}{5}$$

3 ni olish uchun 15 ni 5 ga bo‘ling.

$$x=3$$