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

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

x uchun yechish

$$x=-2$$

$$x=0$$

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, 1+x,1-x ning eng kichik karralisiga ko‘paytiring.

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

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

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

-2x+2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

-3 hosil qilish uchun -1 va 3 ni ko'paytirish.

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

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

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

-3-3x teskarisini topish uchun har birining teskarisini toping.

$$-2x^{2}+2=x-1+3+3x$$

2 olish uchun -1 va 3'ni qo'shing.

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

4x ni olish uchun x va 3x ni birlashtirish.

$$-2x^{2}+2=4x+2$$

Ikkala tarafdan 4x ni ayirish.

$$-2x^{2}+2-4x=2$$

Ikkala tarafdan 2 ni ayirish.

$$-2x^{2}+2-4x-2=0$$

0 olish uchun 2 dan 2 ni ayirish.

$$-2x^{2}-4x=0$$

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

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

\left(-4\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±4}{2\left(-2\right)}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±4}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{4±4}{-4}$$

x=\frac{4±4}{-4} tenglamasini yeching, bunda ± musbat. 4 ni 4 ga qo'shish.

$$x=\frac{8}{-4}$$

8 ni -4 ga bo'lish.

$$x=-2$$

x=\frac{4±4}{-4} tenglamasini yeching, bunda ± manfiy. 4 dan 4 ni ayirish.

$$x=\frac{0}{-4}$$

0 ni -4 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-2 x=0$$

Kvadratni yakunlash 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, 1+x,1-x ning eng kichik karralisiga ko‘paytiring.

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

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

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

-2x+2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

-3 hosil qilish uchun -1 va 3 ni ko'paytirish.

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

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

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

-3-3x teskarisini topish uchun har birining teskarisini toping.

$$-2x^{2}+2=x-1+3+3x$$

2 olish uchun -1 va 3'ni qo'shing.

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

4x ni olish uchun x va 3x ni birlashtirish.

$$-2x^{2}+2=4x+2$$

Ikkala tarafdan 4x ni ayirish.

$$-2x^{2}+2-4x=2$$

Ikkala tarafdan 2 ni ayirish.

$$-2x^{2}-4x=2-2$$

0 olish uchun 2 dan 2 ni ayirish.

$$-2x^{2}-4x=0$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}-4x}{-2}=\frac{0}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{4}{-2}\right)x=\frac{0}{-2}$$

-4 ni -2 ga bo'lish.

$$x^{2}+2x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

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

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+2x+1^{2}=1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=1$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{1}$$

Qisqartirish.

$$x+1=1 x+1=-1$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=0 x=-2$$