x+10/x=x-5/x+10 eching

$$\frac { x + 10 } { x } = \frac { x - 5 } { x + 10 }$$

x uchun yechish

$$x=-4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -10,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x+10\right) ga, x,x+10 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+10\right)\left(x+10\right)=x\left(x-5\right)$$

\left(x+10\right)^{2} hosil qilish uchun x+10 va x+10 ni ko'paytirish.

$$\left(x+10\right)^{2}=x\left(x-5\right)$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+10\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+20x+100=x\left(x-5\right)$$

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

$$x^{2}+20x+100=x^{2}-5x$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}+20x+100-x^{2}=-5x$$

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

$$20x+100=-5x$$

5x ni ikki tarafga qo’shing.

$$20x+100+5x=0$$

25x ni olish uchun 20x va 5x ni birlashtirish.

$$25x+100=0$$

Ikkala tarafdan 100 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$25x=-100$$

Ikki tarafini 25 ga bo‘ling.

$$x=\frac{-100}{25}$$

-4 ni olish uchun -100 ni 25 ga bo‘ling.

$$x=-4$$