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

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

x uchun yechish

$$x=-1$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

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

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

x-3 ga 2x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

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

-3x ni olish uchun 2x va -5x ni birlashtirish.

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

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

$$3x^{2}-3x-3=3x+6$$

Ikkala tarafdan 3x ni ayirish.

$$3x^{2}-3x-3-3x=6$$

-6x ni olish uchun -3x va -3x ni birlashtirish.

$$3x^{2}-6x-3=6$$

Ikkala tarafdan 6 ni ayirish.

$$3x^{2}-6x-3-6=0$$

-9 olish uchun -3 dan 6 ni ayirish.

$$3x^{2}-6x-9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -6 ni b va -9 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 3\left(-9\right)}}{2\times 3}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 3\left(-9\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-12\left(-9\right)}}{2\times 3}$$

-12 ni -9 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+108}}{2\times 3}$$

36 ni 108 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{144}}{2\times 3}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±12}{2\times 3}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±12}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{6±12}{6}$$

x=\frac{6±12}{6} tenglamasini yeching, bunda ± musbat. 6 ni 12 ga qo'shish.

$$x=\frac{18}{6}$$

18 ni 6 ga bo'lish.

$$x=3$$

x=\frac{6±12}{6} tenglamasini yeching, bunda ± manfiy. 6 dan 12 ni ayirish.

$$x=-\frac{6}{6}$$

-6 ni 6 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=3 x=-1$$

x qiymati 3 teng bo‘lmaydi.

$$x=-1$$

Kvadratni yakunlash bo'yicha qadamlar

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

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

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

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

x-3 ga 2x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

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

-3x ni olish uchun 2x va -5x ni birlashtirish.

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

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

$$3x^{2}-3x-3=3x+6$$

Ikkala tarafdan 3x ni ayirish.

$$3x^{2}-3x-3-3x=6$$

-6x ni olish uchun -3x va -3x ni birlashtirish.

$$3x^{2}-6x-3=6$$

3 ni ikki tarafga qo’shing.

$$3x^{2}-6x=6+3$$

9 olish uchun 6 va 3'ni qo'shing.

$$3x^{2}-6x=9$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-6x}{3}=\frac{9}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{6}{3}\right)x=\frac{9}{3}$$

-6 ni 3 ga bo'lish.

$$x^{2}-2x=\frac{9}{3}$$

9 ni 3 ga bo'lish.

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

-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.

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

3 ni 1 ga qo'shish.

$$x^{2}-2x+1=4$$

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.

$$\left(x-1\right)^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{4}$$

Qisqartirish.

$$x-1=2 x-1=-2$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=3 x=-1$$

x qiymati 3 teng bo‘lmaydi.

$$x=-1$$