x+3/x-2-2x+5/2x-4=3+2/2 eching

$$\frac{ x+3 }{ x-2 } - \frac{ 2x+5 }{ 2x-4 } = 3+ \frac{ 2 }{ 2 }$$

x uchun yechish

$$x = \frac{17}{8} = 2\frac{1}{8} = 2,125$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(x-2\right) ga, x-2,2x-4,2 ning eng kichik karralisiga ko‘paytiring.

$$2\left(x+3\right)-\left(2x+5\right)=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

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

$$2x+6-\left(2x+5\right)=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

2x+5 teskarisini topish uchun har birining teskarisini toping.

$$2x+6-2x-5=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

0 ni olish uchun 2x va -2x ni birlashtirish.

$$6-5=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

1 olish uchun 6 dan 5 ni ayirish.

$$1=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$1=6\left(x-2\right)+\left(x-2\right)\times 2$$

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

$$1=6x-12+\left(x-2\right)\times 2$$

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

$$1=6x-12+2x-4$$

8x ni olish uchun 6x va 2x ni birlashtirish.

$$1=8x-12-4$$

-16 olish uchun -12 dan 4 ni ayirish.

$$1=8x-16$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$8x-16=1$$

16 ni ikki tarafga qo’shing.

$$8x=1+16$$

17 olish uchun 1 va 16'ni qo'shing.

$$8x=17$$

Ikki tarafini 8 ga bo‘ling.

$$x=\frac{17}{8}$$