x-3/x+2+x-2/x-3=2x^2-5x-6/x^2-x-6 eching

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

x uchun yechish

$$x=11$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -2,3 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-3\right)\left(x+2\right) ga, x+2,x-3,x^{2}-x-6 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-3\right)\left(x-3\right)+\left(x+2\right)\left(x-2\right)=2x^{2}-5x-6$$

\left(x-3\right)^{2} hosil qilish uchun x-3 va x-3 ni ko'paytirish.

$$\left(x-3\right)^{2}+\left(x+2\right)\left(x-2\right)=2x^{2}-5x-6$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-3\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-6x+9+\left(x+2\right)\left(x-2\right)=2x^{2}-5x-6$$

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.

$$x^{2}-6x+9+x^{2}-4=2x^{2}-5x-6$$

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

$$2x^{2}-6x+9-4=2x^{2}-5x-6$$

5 olish uchun 9 dan 4 ni ayirish.

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

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

$$-6x+5=-5x-6$$

5x ni ikki tarafga qo’shing.

$$-6x+5+5x=-6$$

-x ni olish uchun -6x va 5x ni birlashtirish.

$$-x+5=-6$$

Ikkala tarafdan 5 ni ayirish.

$$-x=-6-5$$

-11 olish uchun -6 dan 5 ni ayirish.

$$-x=-11$$

Ikkala tarafini -1 ga ko‘paytiring.

$$x=11$$