6-x/x+4=x/6-x eching

$$\frac{ 6-x }{ x+4 } = \frac{ x }{ 6-x }$$

x uchun yechish

$$x = \frac{9}{4} = 2\frac{1}{4} = 2,25$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -4,6 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-6\right)\left(x+4\right) ga, x+4,6-x ning eng kichik karralisiga ko‘paytiring.

$$\left(x-6\right)\left(6-x\right)=-\left(4+x\right)x$$

x-6 ga 6-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x-x^{2}-36=-\left(4+x\right)x$$

-1 ga 4+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x-x^{2}-36=\left(-4-x\right)x$$

-4-x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x-x^{2}-36=-4x-x^{2}$$

4x ni ikki tarafga qo’shing.

$$12x-x^{2}-36+4x=-x^{2}$$

16x ni olish uchun 12x va 4x ni birlashtirish.

$$16x-x^{2}-36=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$16x-x^{2}-36+x^{2}=0$$

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

$$16x-36=0$$

36 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$16x=36$$

Ikki tarafini 16 ga bo‘ling.

$$x=\frac{36}{16}$$

\frac{36}{16} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{9}{4}$$