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

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

x uchun yechish

$$x=5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 0,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3x\left(x-2\right) ga, 3x,x-2 ning eng kichik karralisiga ko‘paytiring.

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

Hisoblang: \left(x-2\right)\left(x+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 2 kvadratini chiqarish.

$$x^{2}-4-3x=\left(x-2\right)\left(x-3\right)$$

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

$$x^{2}-4-3x=x^{2}-5x+6$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}-4-3x-x^{2}=-5x+6$$

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

$$-4-3x=-5x+6$$

5x ni ikki tarafga qo’shing.

$$-4-3x+5x=6$$

2x ni olish uchun -3x va 5x ni birlashtirish.

$$-4+2x=6$$

4 ni ikki tarafga qo’shing.

$$2x=6+4$$

10 olish uchun 6 va 4'ni qo'shing.

$$2x=10$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{10}{2}$$

5 ni olish uchun 10 ni 2 ga bo‘ling.

$$x=5$$