3/x+1+2=3/x-1 eching

$$\frac { 3 } { x + 1 } + 2 = \frac { 3 } { x - 1 }$$

x uchun yechish

$$x=2$$

$$x=-2$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati -1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+1\right) ga, x+1,x-1 ning eng kichik karralisiga ko‘paytiring.

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

x-1 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x-1 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

x^{2}-1 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-5 olish uchun -3 dan 2 ni ayirish.

$$3x-5+2x^{2}=\left(x+1\right)\times 3$$

x+1 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-5+2x^{2}=3x+3$$

Ikkala tarafdan 3x ni ayirish.

$$3x-5+2x^{2}-3x=3$$

0 ni olish uchun 3x va -3x ni birlashtirish.

$$-5+2x^{2}=3$$

5 ni ikki tarafga qo’shing.

$$2x^{2}=3+5$$

8 olish uchun 3 va 5'ni qo'shing.

$$2x^{2}=8$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{8}{2}$$

4 ni olish uchun 8 ni 2 ga bo‘ling.

$$x^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2 x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+1\right) ga, x+1,x-1 ning eng kichik karralisiga ko‘paytiring.

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

x-1 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x-1 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

x^{2}-1 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-5 olish uchun -3 dan 2 ni ayirish.

$$3x-5+2x^{2}=\left(x+1\right)\times 3$$

x+1 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-5+2x^{2}=3x+3$$

Ikkala tarafdan 3x ni ayirish.

$$3x-5+2x^{2}-3x=3$$

0 ni olish uchun 3x va -3x ni birlashtirish.

$$-5+2x^{2}=3$$

Ikkala tarafdan 3 ni ayirish.

$$-5+2x^{2}-3=0$$

-8 olish uchun -5 dan 3 ni ayirish.

$$-8+2x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$2x^{2}-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 0 ni b va -8 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-8\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-8\right)}}{2\times 2}$$

-8 ni -8 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{64}}{2\times 2}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±8}{4}$$

x=\frac{0±8}{4} tenglamasini yeching, bunda ± musbat. 8 ni 4 ga bo'lish.

$$x=2$$

x=\frac{0±8}{4} tenglamasini yeching, bunda ± manfiy. -8 ni 4 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

$$x=2 x=-2$$