x^2+6/2x-10-x/2=x/x-5 eching

$$\frac{ { x }^{ 2 } +6 }{ 2x-10 } - \frac{ x }{ 2 } = \frac{ x }{ x-5 }$$

x uchun yechish

$$x=-2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 5 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(x-5\right) ga, 2x-10,2,x-5 ning eng kichik karralisiga ko‘paytiring.

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

x-5 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x^{2}-5x teskarisini topish uchun har birining teskarisini toping.

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

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

$$6+5x=2x$$

Ikkala tarafdan 2x ni ayirish.

$$6+5x-2x=0$$

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

$$6+3x=0$$

Ikkala tarafdan 6 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$3x=-6$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{-6}{3}$$

-2 ni olish uchun -6 ni 3 ga bo‘ling.

$$x=-2$$