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

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

x uchun yechish

$$x=-\frac{1}{3}\approx -0,333333333$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-2 ga, x-2,2-x ning eng kichik karralisiga ko‘paytiring.

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

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

$$3x^{2}-6x-1=-\left(x-1\right)$$

x-1 teskarisini topish uchun har birining teskarisini toping.

$$3x^{2}-6x-1=-x+1$$

x ni ikki tarafga qo’shing.

$$3x^{2}-6x-1+x=1$$

-5x ni olish uchun -6x va x ni birlashtirish.

$$3x^{2}-5x-1=1$$

Ikkala tarafdan 1 ni ayirish.

$$3x^{2}-5x-1-1=0$$

-2 olish uchun -1 dan 1 ni ayirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -5 ni b va -2 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 3\left(-2\right)}}{2\times 3}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 3\left(-2\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25-12\left(-2\right)}}{2\times 3}$$

-12 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25+24}}{2\times 3}$$

25 ni 24 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{49}}{2\times 3}$$

49 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±7}{2\times 3}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±7}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{5±7}{6}$$

x=\frac{5±7}{6} tenglamasini yeching, bunda ± musbat. 5 ni 7 ga qo'shish.

$$x=\frac{12}{6}$$

12 ni 6 ga bo'lish.

$$x=2$$

x=\frac{5±7}{6} tenglamasini yeching, bunda ± manfiy. 5 dan 7 ni ayirish.

$$x=-\frac{2}{6}$$

\frac{-2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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

x qiymati 2 teng bo‘lmaydi.

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

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-2 ga, x-2,2-x ning eng kichik karralisiga ko‘paytiring.

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

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

$$3x^{2}-6x-1=-\left(x-1\right)$$

x-1 teskarisini topish uchun har birining teskarisini toping.

$$3x^{2}-6x-1=-x+1$$

x ni ikki tarafga qo’shing.

$$3x^{2}-6x-1+x=1$$

-5x ni olish uchun -6x va x ni birlashtirish.

$$3x^{2}-5x-1=1$$

1 ni ikki tarafga qo’shing.

$$3x^{2}-5x=1+1$$

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

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

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-5x}{3}=\frac{2}{3}$$

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

$$x^{2}-\frac{5}{3}x=\frac{2}{3}$$

-\frac{5}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{6} olish uchun. Keyin, -\frac{5}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{5}{3}x+\left(-\frac{5}{6}\right)^{2}=\frac{2}{3}+\left(-\frac{5}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{6} kvadratini chiqarish.

$$x^{2}-\frac{5}{3}x+\frac{25}{36}=\frac{2}{3}+\frac{25}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{2}{3} ni \frac{25}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{5}{3}x+\frac{25}{36}=\frac{49}{36}$$

x^{2}-\frac{5}{3}x+\frac{25}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{5}{6}\right)^{2}=\frac{49}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{6}\right)^{2}}=\sqrt{\frac{49}{36}}$$

Qisqartirish.

$$x-\frac{5}{6}=\frac{7}{6} x-\frac{5}{6}=-\frac{7}{6}$$

\frac{5}{6} ni tenglamaning ikkala tarafiga qo'shish.

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

x qiymati 2 teng bo‘lmaydi.

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