2x-7/x-4-x+2/x+1=x+6/(x-4)(x+1) eching

$$\frac { 2 x - 7 } { x - 4 } - \frac { x + 2 } { x + 1 } = \frac { x + 6 } { ( x - 4 ) ( x + 1 ) }$$

x uchun yechish

$$x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -1,4 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-4\right)\left(x+1\right) ga, x-4,x+1,\left(x-4\right)\left(x+1\right) ning eng kichik karralisiga ko‘paytiring.

$$\left(x+1\right)\left(2x-7\right)-\left(x-4\right)\left(x+2\right)=x+6$$

x+1 ga 2x-7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-5x-7-\left(x-4\right)\left(x+2\right)=x+6$$

x-4 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-5x-7-\left(x^{2}-2x-8\right)=x+6$$

x^{2}-2x-8 teskarisini topish uchun har birining teskarisini toping.

$$2x^{2}-5x-7-x^{2}+2x+8=x+6$$

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

$$x^{2}-5x-7+2x+8=x+6$$

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

$$x^{2}-3x-7+8=x+6$$

1 olish uchun -7 va 8'ni qo'shing.

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

Ikkala tarafdan x ni ayirish.

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

-4x ni olish uchun -3x va -x ni birlashtirish.

$$x^{2}-4x+1=6$$

Ikkala tarafdan 6 ni ayirish.

$$x^{2}-4x+1-6=0$$

-5 olish uchun 1 dan 6 ni ayirish.

$$x^{2}-4x-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -4 ni b va -5 ni c bilan almashtiring.

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

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-5\right)}}{2}$$

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+20}}{2}$$

16 ni 20 ga qo'shish.

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

36 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±6}{2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±6}{2}$$

x=\frac{4±6}{2} tenglamasini yeching, bunda ± musbat. 4 ni 6 ga qo'shish.

$$x=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$x=5$$

x=\frac{4±6}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 6 ni ayirish.

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

-2 ni 2 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=5 x=-1$$

x qiymati -1 teng bo‘lmaydi.

$$x=5$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -1,4 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-4\right)\left(x+1\right) ga, x-4,x+1,\left(x-4\right)\left(x+1\right) ning eng kichik karralisiga ko‘paytiring.

$$\left(x+1\right)\left(2x-7\right)-\left(x-4\right)\left(x+2\right)=x+6$$

x+1 ga 2x-7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-5x-7-\left(x-4\right)\left(x+2\right)=x+6$$

x-4 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-5x-7-\left(x^{2}-2x-8\right)=x+6$$

x^{2}-2x-8 teskarisini topish uchun har birining teskarisini toping.

$$2x^{2}-5x-7-x^{2}+2x+8=x+6$$

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

$$x^{2}-5x-7+2x+8=x+6$$

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

$$x^{2}-3x-7+8=x+6$$

1 olish uchun -7 va 8'ni qo'shing.

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

Ikkala tarafdan x ni ayirish.

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

-4x ni olish uchun -3x va -x ni birlashtirish.

$$x^{2}-4x+1=6$$

Ikkala tarafdan 1 ni ayirish.

$$x^{2}-4x=6-1$$

5 olish uchun 6 dan 1 ni ayirish.

$$x^{2}-4x=5$$

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

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

-2 kvadratini chiqarish.

$$x^{2}-4x+4=5+4$$

5 ni 4 ga qo'shish.

$$x^{2}-4x+4=9$$

x^{2}-4x+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-2\right)^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{9}$$

Qisqartirish.

$$x-2=3 x-2=-3$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=5 x=-1$$

x qiymati -1 teng bo‘lmaydi.

$$x=5$$