y-3/y-5=y-1/y-7 eching

$$\frac { y - 3 } { y - 5 } = \frac { y - 1 } { y - 7 }$$

y uchun yechish

$$y=4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 5,7 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(y-7\right)\left(y-5\right) ga, y-5,y-7 ning eng kichik karralisiga ko‘paytiring.

$$\left(y-7\right)\left(y-3\right)=\left(y-5\right)\left(y-1\right)$$

y-7 ga y-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$y^{2}-10y+21=\left(y-5\right)\left(y-1\right)$$

y-5 ga y-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$y^{2}-10y+21=y^{2}-6y+5$$

Ikkala tarafdan y^{2} ni ayirish.

$$y^{2}-10y+21-y^{2}=-6y+5$$

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

$$-10y+21=-6y+5$$

6y ni ikki tarafga qo’shing.

$$-10y+21+6y=5$$

-4y ni olish uchun -10y va 6y ni birlashtirish.

$$-4y+21=5$$

Ikkala tarafdan 21 ni ayirish.

$$-4y=5-21$$

-16 olish uchun 5 dan 21 ni ayirish.

$$-4y=-16$$

Ikki tarafini -4 ga bo‘ling.

$$y=\frac{-16}{-4}$$

4 ni olish uchun -16 ni -4 ga bo‘ling.

$$y=4$$