1/x+3-2/5x-20=3/2(3x-12)-2/x+3 eching

$$\frac { 1 } { x + 3 } - \frac { 2 } { 5 x - 20 } = \frac { 3 } { 2 ( 3 x - 12 ) } - \frac { 2 } { x + 3 }$$

x uchun yechish

$$x=7$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -3,4 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 30\left(x-4\right)\left(x+3\right) ga, x+3,5x-20,2\left(3x-12\right) ning eng kichik karralisiga ko‘paytiring.

$$30x-120-\left(6x+18\right)\times 2=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

6x+18 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$30x-120-\left(12x+36\right)=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

12x+36 teskarisini topish uchun har birining teskarisini toping.

$$30x-120-12x-36=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

18x ni olish uchun 30x va -12x ni birlashtirish.

$$18x-120-36=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

-156 olish uchun -120 dan 36 ni ayirish.

$$18x-156=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

5x+15 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x-156=15x+45-\left(30x-120\right)\times 2$$

30x-120 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x-156=15x+45-\left(60x-240\right)$$

60x-240 teskarisini topish uchun har birining teskarisini toping.

$$18x-156=15x+45-60x+240$$

-45x ni olish uchun 15x va -60x ni birlashtirish.

$$18x-156=-45x+45+240$$

285 olish uchun 45 va 240'ni qo'shing.

$$18x-156=-45x+285$$

45x ni ikki tarafga qo’shing.

$$18x-156+45x=285$$

63x ni olish uchun 18x va 45x ni birlashtirish.

$$63x-156=285$$

156 ni ikki tarafga qo’shing.

$$63x=285+156$$

441 olish uchun 285 va 156'ni qo'shing.

$$63x=441$$

Ikki tarafini 63 ga bo‘ling.

$$x=\frac{441}{63}$$

7 ni olish uchun 441 ni 63 ga bo‘ling.

$$x=7$$