3x/x+1+6/2x=7/x eching

$$\frac { 3 x } { x + 1 } + \frac { 6 } { 2 x } = \frac { 7 } { x }$$

x uchun yechish

$$x=-\frac{2}{3}\approx -0,666666667$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -1,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x\left(x+1\right) ga, x+1,2x,x ning eng kichik karralisiga ko‘paytiring.

$$2x\times 3x+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$6xx+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$6x^{2}+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

x+1 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

2x+2 ga 7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}+6x+6=14x+14$$

Ikkala tarafdan 14x ni ayirish.

$$6x^{2}+6x+6-14x=14$$

-8x ni olish uchun 6x va -14x ni birlashtirish.

$$6x^{2}-8x+6=14$$

Ikkala tarafdan 14 ni ayirish.

$$6x^{2}-8x+6-14=0$$

-8 olish uchun 6 dan 14 ni ayirish.

$$6x^{2}-8x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -8 ni b va -8 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 6\left(-8\right)}}{2\times 6}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 6\left(-8\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-24\left(-8\right)}}{2\times 6}$$

-24 ni -8 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+192}}{2\times 6}$$

64 ni 192 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{256}}{2\times 6}$$

256 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±16}{2\times 6}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±16}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{8±16}{12}$$

x=\frac{8±16}{12} tenglamasini yeching, bunda ± musbat. 8 ni 16 ga qo'shish.

$$x=\frac{24}{12}$$

24 ni 12 ga bo'lish.

$$x=2$$

x=\frac{8±16}{12} tenglamasini yeching, bunda ± manfiy. 8 dan 16 ni ayirish.

$$x=-\frac{8}{12}$$

\frac{-8}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -1,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x\left(x+1\right) ga, x+1,2x,x ning eng kichik karralisiga ko‘paytiring.

$$2x\times 3x+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$6xx+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$6x^{2}+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

x+1 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

2x+2 ga 7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}+6x+6=14x+14$$

Ikkala tarafdan 14x ni ayirish.

$$6x^{2}+6x+6-14x=14$$

-8x ni olish uchun 6x va -14x ni birlashtirish.

$$6x^{2}-8x+6=14$$

Ikkala tarafdan 6 ni ayirish.

$$6x^{2}-8x=14-6$$

8 olish uchun 14 dan 6 ni ayirish.

$$6x^{2}-8x=8$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-8x}{6}=\frac{8}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

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

\frac{-8}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{4}{3}x=\frac{8}{6}$$

\frac{8}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{4}{3}x=\frac{4}{3}$$

-\frac{4}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{2}{3} olish uchun. Keyin, -\frac{2}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{2}{3} kvadratini chiqarish.

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

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{4}{3} ni \frac{4}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{4}{3}x+\frac{4}{9}=\frac{16}{9}$$

x^{2}-\frac{4}{3}x+\frac{4}{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.

$$\left(x-\frac{2}{3}\right)^{2}=\frac{16}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{2}{3}\right)^{2}}=\sqrt{\frac{16}{9}}$$

Qisqartirish.

$$x-\frac{2}{3}=\frac{4}{3} x-\frac{2}{3}=-\frac{4}{3}$$

\frac{2}{3} ni tenglamaning ikkala tarafiga qo'shish.

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