x-24/2x^2-9x-18=x/x-6-2x/2x+3 eching

$$\frac { x - 24 } { 2 x ^ { 2 } - 9 x - 18 } = \frac { x } { x - 6 } - \frac { 2 x } { 2 x + 3 }$$

x uchun yechish

$$x = -\frac{12}{7} = -1\frac{5}{7} \approx -1,714285714$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -\frac{3}{2},6 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-6\right)\left(2x+3\right) ga, 2x^{2}-9x-18,x-6,2x+3 ning eng kichik karralisiga ko‘paytiring.

$$x-24=\left(2x+3\right)x-\left(x-6\right)\times 2x$$

2x+3 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x-24=2x^{2}+3x-\left(x-6\right)\times 2x$$

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

$$x-24=2x^{2}+3x-\left(2x-12\right)x$$

2x-12 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x-24=2x^{2}+3x-\left(2x^{2}-12x\right)$$

2x^{2}-12x teskarisini topish uchun har birining teskarisini toping.

$$x-24=2x^{2}+3x-2x^{2}+12x$$

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

$$x-24=3x+12x$$

15x ni olish uchun 3x va 12x ni birlashtirish.

$$x-24=15x$$

Ikkala tarafdan 15x ni ayirish.

$$x-24-15x=0$$

-14x ni olish uchun x va -15x ni birlashtirish.

$$-14x-24=0$$

24 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-14x=24$$

Ikki tarafini -14 ga bo‘ling.

$$x=\frac{24}{-14}$$

\frac{24}{-14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{12}{7}$$