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

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

x uchun yechish

$$x=1$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati -1,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x+1\right) ga, x,x+1 ning eng kichik karralisiga ko‘paytiring.

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

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

$$2x+2-x\times 2x=x\times 2$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$2x+2-x^{2}\times 2=x\times 2$$

Ikkala tarafdan x\times 2 ni ayirish.

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

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

$$2-x^{2}\times 2=0$$

Ikkala tarafdan 2 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-x^{2}\times 2=-2$$

Ikki tarafini -1 ga bo‘ling.

$$x^{2}\times 2=\frac{-2}{-1}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-2}{-1} kasrini 2 ga soddalashtirish mumkin.

$$x^{2}\times 2=2$$

Ikki tarafini 2 ga bo‘ling.

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

1 ni olish uchun 2 ni 2 ga bo‘ling.

$$x^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=1 x=-1$$

x qiymati -1 teng bo‘lmaydi.

$$x=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -1,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x+1\right) ga, x,x+1 ning eng kichik karralisiga ko‘paytiring.

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

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

$$2x+2-x\times 2x=x\times 2$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$2x+2-x^{2}\times 2=x\times 2$$

Ikkala tarafdan x\times 2 ni ayirish.

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

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

$$2-x^{2}\times 2=0$$

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

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

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.

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

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 2 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

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

8 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16}}{2\left(-2\right)}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±4}{-4}$$

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

$$x=-1$$

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

$$x=1$$

Tenglama yechildi.

$$x=-1 x=1$$

x qiymati -1 teng bo‘lmaydi.

$$x=1$$