9/2x+1-8x/2x-1=-4 eching

$$\frac { 9 } { 2 x + 1 } - \frac { 8 x } { 2 x - 1 } = - 4$$

x uchun yechish

$$x = \frac{13}{10} = 1\frac{3}{10} = 1,3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$\left(2x-1\right)\times 9-\left(2x+1\right)\times 8x=-4\left(2x-1\right)\left(2x+1\right)$$

2x-1 ga 9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x-9-\left(2x+1\right)\times 8x=-4\left(2x-1\right)\left(2x+1\right)$$

2x+1 ga 8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x-9-\left(16x+8\right)x=-4\left(2x-1\right)\left(2x+1\right)$$

16x+8 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x-9-\left(16x^{2}+8x\right)=-4\left(2x-1\right)\left(2x+1\right)$$

16x^{2}+8x teskarisini topish uchun har birining teskarisini toping.

$$18x-9-16x^{2}-8x=-4\left(2x-1\right)\left(2x+1\right)$$

10x ni olish uchun 18x va -8x ni birlashtirish.

$$10x-9-16x^{2}=-4\left(2x-1\right)\left(2x+1\right)$$

-4 ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10x-9-16x^{2}=\left(-8x+4\right)\left(2x+1\right)$$

-8x+4 ga 2x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$10x-9-16x^{2}=-16x^{2}+4$$

16x^{2} ni ikki tarafga qo’shing.

$$10x-9-16x^{2}+16x^{2}=4$$

0 ni olish uchun -16x^{2} va 16x^{2} ni birlashtirish.

$$10x-9=4$$

9 ni ikki tarafga qo’shing.

$$10x=4+9$$

13 olish uchun 4 va 9'ni qo'shing.

$$10x=13$$

Ikki tarafini 10 ga bo‘ling.

$$x=\frac{13}{10}$$