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

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

x uchun yechish

$$x=\sqrt{19}\approx 4,358898944$$

$$x=-\sqrt{19}\approx -4,358898944$$

Kvadrat ildizini topish bo'yicha qadamlar

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

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

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

$$3x+9-\left(x-2\right)\times 2=\left(x-2\right)\left(x+3\right)$$

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

$$3x+9-\left(2x-4\right)=\left(x-2\right)\left(x+3\right)$$

2x-4 teskarisini topish uchun har birining teskarisini toping.

$$3x+9-2x+4=\left(x-2\right)\left(x+3\right)$$

x ni olish uchun 3x va -2x ni birlashtirish.

$$x+9+4=\left(x-2\right)\left(x+3\right)$$

13 olish uchun 9 va 4'ni qo'shing.

$$x+13=\left(x-2\right)\left(x+3\right)$$

x-2 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x+13=x^{2}+x-6$$

Ikkala tarafdan x^{2} ni ayirish.

$$x+13-x^{2}=x-6$$

Ikkala tarafdan x ni ayirish.

$$x+13-x^{2}-x=-6$$

0 ni olish uchun x va -x ni birlashtirish.

$$13-x^{2}=-6$$

Ikkala tarafdan 13 ni ayirish.

$$-x^{2}=-6-13$$

-19 olish uchun -6 dan 13 ni ayirish.

$$-x^{2}=-19$$

Ikki tarafini -1 ga bo‘ling.

$$x^{2}=\frac{-19}{-1}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-19}{-1} kasrini 19 ga soddalashtirish mumkin.

$$x^{2}=19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{19} x=-\sqrt{19}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

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

$$3x+9-\left(x-2\right)\times 2=\left(x-2\right)\left(x+3\right)$$

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

$$3x+9-\left(2x-4\right)=\left(x-2\right)\left(x+3\right)$$

2x-4 teskarisini topish uchun har birining teskarisini toping.

$$3x+9-2x+4=\left(x-2\right)\left(x+3\right)$$

x ni olish uchun 3x va -2x ni birlashtirish.

$$x+9+4=\left(x-2\right)\left(x+3\right)$$

13 olish uchun 9 va 4'ni qo'shing.

$$x+13=\left(x-2\right)\left(x+3\right)$$

x-2 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x+13=x^{2}+x-6$$

Ikkala tarafdan x^{2} ni ayirish.

$$x+13-x^{2}=x-6$$

Ikkala tarafdan x ni ayirish.

$$x+13-x^{2}-x=-6$$

0 ni olish uchun x va -x ni birlashtirish.

$$13-x^{2}=-6$$

6 ni ikki tarafga qo’shing.

$$13-x^{2}+6=0$$

19 olish uchun 13 va 6'ni qo'shing.

$$19-x^{2}=0$$

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.

$$-x^{2}+19=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 0 ni b va 19 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{4\times 19}}{2\left(-1\right)}$$

4 ni 19 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{76}}{2\left(-1\right)}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{19}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{19}}{-2}$$

x=\frac{0±2\sqrt{19}}{-2} tenglamasini yeching, bunda ± musbat.

$$x=-\sqrt{19}$$

x=\frac{0±2\sqrt{19}}{-2} tenglamasini yeching, bunda ± manfiy.

$$x=\sqrt{19}$$

Tenglama yechildi.

$$x=-\sqrt{19} x=\sqrt{19}$$