2/3-6x^2/9x^2-1=2/3x-1 eching

$$\frac { 2 } { 3 } - \frac { 6 x ^ { 2 } } { 9 x ^ { 2 } - 1 } = \frac { 2 } { 3 x - 1 }$$

x uchun yechish

$$x=-\frac{4}{9}\approx -0,444444444$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -\frac{1}{3},\frac{1}{3} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3\left(3x-1\right)\left(3x+1\right) ga, 3,9x^{2}-1,3x-1 ning eng kichik karralisiga ko‘paytiring.

$$3\left(3x-1\right)\left(3x+1\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

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

$$\left(9x-3\right)\left(3x+1\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

9x-3 ga 3x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(27x^{2}-3\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

27x^{2}-3 ga \frac{2}{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}-2-3\times 6x^{2}=\left(9x+3\right)\times 2$$

-18 hosil qilish uchun -3 va 6 ni ko'paytirish.

$$18x^{2}-2-18x^{2}=\left(9x+3\right)\times 2$$

0 ni olish uchun 18x^{2} va -18x^{2} ni birlashtirish.

$$-2=\left(9x+3\right)\times 2$$

9x+3 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-2=18x+6$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$18x+6=-2$$

Ikkala tarafdan 6 ni ayirish.

$$18x=-2-6$$

-8 olish uchun -2 dan 6 ni ayirish.

$$18x=-8$$

Ikki tarafini 18 ga bo‘ling.

$$x=\frac{-8}{18}$$

\frac{-8}{18} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{4}{9}$$