x+4/x=x/x+4 eching

$$\frac{ x+4 }{ x } = \frac{ x }{ x+4 }$$

x uchun yechish

$$x=-2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -4,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x+4\right) ga, x,x+4 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+4\right)\left(x+4\right)=xx$$

\left(x+4\right)^{2} hosil qilish uchun x+4 va x+4 ni ko'paytirish.

$$\left(x+4\right)^{2}=xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+4\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+8x+16=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}+8x+16-x^{2}=0$$

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

$$8x+16=0$$

Ikkala tarafdan 16 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$8x=-16$$

Ikki tarafini 8 ga bo‘ling.

$$x=\frac{-16}{8}$$

-2 ni olish uchun -16 ni 8 ga bo‘ling.

$$x=-2$$