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

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

x uchun yechish

$$x = -\frac{5}{4} = -1\frac{1}{4} = -1,25$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

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

2x+1 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+3x-2=2x^{2}+7x+3$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$2x^{2}+3x-2-2x^{2}=7x+3$$

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

$$3x-2=7x+3$$

Ikkala tarafdan 7x ni ayirish.

$$3x-2-7x=3$$

-4x ni olish uchun 3x va -7x ni birlashtirish.

$$-4x-2=3$$

2 ni ikki tarafga qo’shing.

$$-4x=3+2$$

5 olish uchun 3 va 2'ni qo'shing.

$$-4x=5$$

Ikki tarafini -4 ga bo‘ling.

$$x=\frac{5}{-4}$$

\frac{5}{-4} kasri manfiy belgini olib tashlash bilan -\frac{5}{4} sifatida qayta yozilishi mumkin.

$$x=-\frac{5}{4}$$