x+3/x+9+7/x-9=7/x-9 eching

$$\frac { x + 3 } { x + 9 } + \frac { 7 } { x - 9 } = \frac { 7 } { x - 9 }$$

x uchun yechish

$$x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -9,9 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-9\right)\left(x+9\right) ga, x+9,x-9 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-9\right)\left(x+3\right)+\left(x+9\right)\times 7=\left(x+9\right)\times 7$$

x-9 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-6x-27+\left(x+9\right)\times 7=\left(x+9\right)\times 7$$

x+9 ga 7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-6x-27+7x+63=\left(x+9\right)\times 7$$

x ni olish uchun -6x va 7x ni birlashtirish.

$$x^{2}+x-27+63=\left(x+9\right)\times 7$$

36 olish uchun -27 va 63'ni qo'shing.

$$x^{2}+x+36=\left(x+9\right)\times 7$$

x+9 ga 7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+x+36=7x+63$$

Ikkala tarafdan 7x ni ayirish.

$$x^{2}+x+36-7x=63$$

-6x ni olish uchun x va -7x ni birlashtirish.

$$x^{2}-6x+36=63$$

Ikkala tarafdan 63 ni ayirish.

$$x^{2}-6x+36-63=0$$

-27 olish uchun 36 dan 63 ni ayirish.

$$x^{2}-6x-27=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va -27 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-27\right)}}{2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-27\right)}}{2}$$

-4 ni -27 marotabaga ko'paytirish.

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

36 ni 108 ga qo'shish.

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

144 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±12}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±12}{2}$$

x=\frac{6±12}{2} tenglamasini yeching, bunda ± musbat. 6 ni 12 ga qo'shish.

$$x=\frac{18}{2}$$

18 ni 2 ga bo'lish.

$$x=9$$

x=\frac{6±12}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 12 ni ayirish.

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

-6 ni 2 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=9 x=-3$$

x qiymati 9 teng bo‘lmaydi.

$$x=-3$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -9,9 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-9\right)\left(x+9\right) ga, x+9,x-9 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-9\right)\left(x+3\right)+\left(x+9\right)\times 7=\left(x+9\right)\times 7$$

x-9 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-6x-27+\left(x+9\right)\times 7=\left(x+9\right)\times 7$$

x+9 ga 7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-6x-27+7x+63=\left(x+9\right)\times 7$$

x ni olish uchun -6x va 7x ni birlashtirish.

$$x^{2}+x-27+63=\left(x+9\right)\times 7$$

36 olish uchun -27 va 63'ni qo'shing.

$$x^{2}+x+36=\left(x+9\right)\times 7$$

x+9 ga 7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+x+36=7x+63$$

Ikkala tarafdan 7x ni ayirish.

$$x^{2}+x+36-7x=63$$

-6x ni olish uchun x va -7x ni birlashtirish.

$$x^{2}-6x+36=63$$

Ikkala tarafdan 36 ni ayirish.

$$x^{2}-6x=63-36$$

27 olish uchun 63 dan 36 ni ayirish.

$$x^{2}-6x=27$$

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

$$x^{2}-6x+\left(-3\right)^{2}=27+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=27+9$$

27 ni 9 ga qo'shish.

$$x^{2}-6x+9=36$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{36}$$

Qisqartirish.

$$x-3=6 x-3=-6$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=9 x=-3$$

x qiymati 9 teng bo‘lmaydi.

$$x=-3$$