x+1/x-1=2x-5/2x-7 eching

$$\frac { x + 1 } { x - 1 } = \frac { 2 x - 5 } { 2 x - 7 }$$

x uchun yechish

$$x=6$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 1,\frac{7}{2} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(2x-7\right) ga, x-1,2x-7 ning eng kichik karralisiga ko‘paytiring.

$$\left(2x-7\right)\left(x+1\right)=\left(x-1\right)\left(2x-5\right)$$

2x-7 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-5x-7=\left(x-1\right)\left(2x-5\right)$$

x-1 ga 2x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-5x-7=2x^{2}-7x+5$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$2x^{2}-5x-7-2x^{2}=-7x+5$$

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

$$-5x-7=-7x+5$$

7x ni ikki tarafga qo’shing.

$$-5x-7+7x=5$$

2x ni olish uchun -5x va 7x ni birlashtirish.

$$2x-7=5$$

7 ni ikki tarafga qo’shing.

$$2x=5+7$$

12 olish uchun 5 va 7'ni qo'shing.

$$2x=12$$

Ikki tarafini 2 ga bo‘ling.

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

6 ni olish uchun 12 ni 2 ga bo‘ling.

$$x=6$$