2x-9/x+4=3x-6/x+4 eching

$$2 x - \frac { 9 } { x + 4 } = \frac { 3 x - 6 } { x + 4 }$$

x uchun yechish

$$x=-3$$

$$x=\frac{1}{2}=0,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+4 ga ko'paytirish.

$$2x\left(x+4\right)-9=3x-6$$

2x ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+8x-9=3x-6$$

Ikkala tarafdan 3x ni ayirish.

$$2x^{2}+8x-9-3x=-6$$

5x ni olish uchun 8x va -3x ni birlashtirish.

$$2x^{2}+5x-9=-6$$

6 ni ikki tarafga qo’shing.

$$2x^{2}+5x-9+6=0$$

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

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

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

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

5 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25-8\left(-3\right)}}{2\times 2}$$

-8 ni -3 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+24}}{2\times 2}$$

25 ni 24 ga qo'shish.

$$x=\frac{-5±\sqrt{49}}{2\times 2}$$

49 ning kvadrat ildizini chiqarish.

$$x=\frac{-5±7}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-5±7}{4}$$

x=\frac{-5±7}{4} tenglamasini yeching, bunda ± musbat. -5 ni 7 ga qo'shish.

$$x=\frac{2}{4}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x=\frac{-5±7}{4} tenglamasini yeching, bunda ± manfiy. -5 dan 7 ni ayirish.

$$x=-\frac{12}{4}$$

-12 ni 4 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+4 ga ko'paytirish.

$$2x\left(x+4\right)-9=3x-6$$

2x ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+8x-9=3x-6$$

Ikkala tarafdan 3x ni ayirish.

$$2x^{2}+8x-9-3x=-6$$

5x ni olish uchun 8x va -3x ni birlashtirish.

$$2x^{2}+5x-9=-6$$

9 ni ikki tarafga qo’shing.

$$2x^{2}+5x=-6+9$$

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

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

Ikki tarafini 2 ga bo‘ling.

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

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

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

\frac{5}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{4} olish uchun. Keyin, \frac{5}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{5}{2}x+\left(\frac{5}{4}\right)^{2}=\frac{3}{2}+\left(\frac{5}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{4} kvadratini chiqarish.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{3}{2}+\frac{25}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni \frac{25}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{49}{16}$$

x^{2}+\frac{5}{2}x+\frac{25}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{5}{4}\right)^{2}=\frac{49}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Qisqartirish.

$$x+\frac{5}{4}=\frac{7}{4} x+\frac{5}{4}=-\frac{7}{4}$$

Tenglamaning ikkala tarafidan \frac{5}{4} ni ayirish.

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