15/x+9x-7/x+2=9 eching

$$\frac { 15 } { x } + \frac { 9 x - 7 } { x + 2 } = 9$$

x uchun yechish

$$x=3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -2,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x+2\right) ga, x,x+2 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+2\right)\times 15+x\left(9x-7\right)=9x\left(x+2\right)$$

x+2 ga 15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$15x+30+x\left(9x-7\right)=9x\left(x+2\right)$$

x ga 9x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$15x+30+9x^{2}-7x=9x\left(x+2\right)$$

8x ni olish uchun 15x va -7x ni birlashtirish.

$$8x+30+9x^{2}=9x\left(x+2\right)$$

9x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8x+30+9x^{2}=9x^{2}+18x$$

Ikkala tarafdan 9x^{2} ni ayirish.

$$8x+30+9x^{2}-9x^{2}=18x$$

0 ni olish uchun 9x^{2} va -9x^{2} ni birlashtirish.

$$8x+30=18x$$

Ikkala tarafdan 18x ni ayirish.

$$8x+30-18x=0$$

-10x ni olish uchun 8x va -18x ni birlashtirish.

$$-10x+30=0$$

Ikkala tarafdan 30 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-10x=-30$$

Ikki tarafini -10 ga bo‘ling.

$$x=\frac{-30}{-10}$$

3 ni olish uchun -30 ni -10 ga bo‘ling.

$$x=3$$