u+10/u+1=u-6/u+9 eching

$$\frac { u + 10 } { u + 1 } = \frac { u - 6 } { u + 9 }$$

u uchun yechish

$$u=-4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

u qiymati -9,-1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(u+1\right)\left(u+9\right) ga, u+1,u+9 ning eng kichik karralisiga ko‘paytiring.

$$\left(u+9\right)\left(u+10\right)=\left(u+1\right)\left(u-6\right)$$

u+9 ga u+10 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$u^{2}+19u+90=\left(u+1\right)\left(u-6\right)$$

u+1 ga u-6 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$u^{2}+19u+90=u^{2}-5u-6$$

Ikkala tarafdan u^{2} ni ayirish.

$$u^{2}+19u+90-u^{2}=-5u-6$$

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

$$19u+90=-5u-6$$

5u ni ikki tarafga qo’shing.

$$19u+90+5u=-6$$

24u ni olish uchun 19u va 5u ni birlashtirish.

$$24u+90=-6$$

Ikkala tarafdan 90 ni ayirish.

$$24u=-6-90$$

-96 olish uchun -6 dan 90 ni ayirish.

$$24u=-96$$

Ikki tarafini 24 ga bo‘ling.

$$u=\frac{-96}{24}$$

-4 ni olish uchun -96 ni 24 ga bo‘ling.

$$u=-4$$