1-3/x/1+frac{3{x}}=2/3 eching

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

x uchun yechish

$$x=15$$

Faktorlash qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{x}{x} va \frac{3}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{x}{x} va \frac{3}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. \frac{x-3}{x} ni \frac{x+3}{x} ga bo'lish \frac{x-3}{x} ga k'paytirish \frac{x+3}{x} ga qaytarish.

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

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

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

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

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

x qiymati -3,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3x\left(x+3\right) ga, x^{2}+3x,3 ning eng kichik karralisiga ko‘paytiring.

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

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

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

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

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

x^{2} ni olish uchun 3x^{2} va -2x^{2} ni birlashtirish.

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

Ikkala tarafdan 6x ni ayirish.

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

-15x ni olish uchun -9x va -6x ni birlashtirish.

$$x^{2}-15x=0$$

x omili.

$$x\left(x-15\right)=0$$

Tenglamani yechish uchun x=0 va x-15=0 ni yeching.

$$x=0 x=15$$

x qiymati 0 teng bo‘lmaydi.

$$x=15$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{x}{x} va \frac{3}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{x}{x} va \frac{3}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. \frac{x-3}{x} ni \frac{x+3}{x} ga bo'lish \frac{x-3}{x} ga k'paytirish \frac{x+3}{x} ga qaytarish.

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

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

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

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

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

Ikkala tarafdan \frac{2}{3} ni ayirish.

$$\frac{x^{2}-3x}{x^{2}+3x}-\frac{2}{3}=0$$

Faktor: x^{2}+3x.

$$\frac{x^{2}-3x}{x\left(x+3\right)}-\frac{2}{3}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x\left(x+3\right) va 3 ning eng kichik umumiy karralisi 3x\left(x+3\right). \frac{x^{2}-3x}{x\left(x+3\right)} ni \frac{3}{3} marotabaga ko'paytirish. \frac{2}{3} ni \frac{x\left(x+3\right)}{x\left(x+3\right)} marotabaga ko'paytirish.

$$\frac{3\left(x^{2}-3x\right)}{3x\left(x+3\right)}-\frac{2x\left(x+3\right)}{3x\left(x+3\right)}=0$$

\frac{3\left(x^{2}-3x\right)}{3x\left(x+3\right)} va \frac{2x\left(x+3\right)}{3x\left(x+3\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3\left(x^{2}-3x\right)-2x\left(x+3\right)}{3x\left(x+3\right)}=0$$

3\left(x^{2}-3x\right)-2x\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{3x^{2}-9x-2x^{2}-6x}{3x\left(x+3\right)}=0$$

3x^{2}-9x-2x^{2}-6x kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}-15x}{3x\left(x+3\right)}=0$$

x qiymati -3,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3x\left(x+3\right) ga ko'paytirish.

$$x^{2}-15x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -15 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}}}{2}$$

\left(-15\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-15\right)±15}{2}$$

-15 ning teskarisi 15 ga teng.

$$x=\frac{15±15}{2}$$

x=\frac{15±15}{2} tenglamasini yeching, bunda ± musbat. 15 ni 15 ga qo'shish.

$$x=\frac{30}{2}$$

30 ni 2 ga bo'lish.

$$x=15$$

x=\frac{15±15}{2} tenglamasini yeching, bunda ± manfiy. 15 dan 15 ni ayirish.

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=15 x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=15$$

Kvadratni yakunlash bo'yicha qadamlar

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{x}{x} va \frac{3}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{x}{x} va \frac{3}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. \frac{x-3}{x} ni \frac{x+3}{x} ga bo'lish \frac{x-3}{x} ga k'paytirish \frac{x+3}{x} ga qaytarish.

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

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

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

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

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

x qiymati -3,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3x\left(x+3\right) ga, x^{2}+3x,3 ning eng kichik karralisiga ko‘paytiring.

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

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

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

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

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

x^{2} ni olish uchun 3x^{2} va -2x^{2} ni birlashtirish.

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

Ikkala tarafdan 6x ni ayirish.

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

-15x ni olish uchun -9x va -6x ni birlashtirish.

$$x^{2}-15x=0$$

-15 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{15}{2} olish uchun. Keyin, -\frac{15}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-15x+\left(-\frac{15}{2}\right)^{2}=\left(-\frac{15}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{15}{2} kvadratini chiqarish.

$$x^{2}-15x+\frac{225}{4}=\frac{225}{4}$$

x^{2}-15x+\frac{225}{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.

$$\left(x-\frac{15}{2}\right)^{2}=\frac{225}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{15}{2}\right)^{2}}=\sqrt{\frac{225}{4}}$$

Qisqartirish.

$$x-\frac{15}{2}=\frac{15}{2} x-\frac{15}{2}=-\frac{15}{2}$$

\frac{15}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=15 x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=15$$