5/x^2+2x-3+45/x^2+10x+21=18/x^2+6x-7 eching

$$\frac { 5 } { x ^ { 2 } + 2 x - 3 } + \frac { 45 } { x ^ { 2 } + 10 x + 21 } = \frac { 18 } { x ^ { 2 } + 6 x - 7 }$$

x uchun yechish

$$x=2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -7,-3,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+3\right)\left(x+7\right) ga, x^{2}+2x-3,x^{2}+10x+21,x^{2}+6x-7 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+7\right)\times 5+\left(x-1\right)\times 45=\left(x+3\right)\times 18$$

x+7 ga 5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5x+35+\left(x-1\right)\times 45=\left(x+3\right)\times 18$$

x-1 ga 45 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5x+35+45x-45=\left(x+3\right)\times 18$$

50x ni olish uchun 5x va 45x ni birlashtirish.

$$50x+35-45=\left(x+3\right)\times 18$$

-10 olish uchun 35 dan 45 ni ayirish.

$$50x-10=\left(x+3\right)\times 18$$

x+3 ga 18 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$50x-10=18x+54$$

Ikkala tarafdan 18x ni ayirish.

$$50x-10-18x=54$$

32x ni olish uchun 50x va -18x ni birlashtirish.

$$32x-10=54$$

10 ni ikki tarafga qo’shing.

$$32x=54+10$$

64 olish uchun 54 va 10'ni qo'shing.

$$32x=64$$

Ikki tarafini 32 ga bo‘ling.

$$x=\frac{64}{32}$$

2 ni olish uchun 64 ni 32 ga bo‘ling.

$$x=2$$