3+15/2+4{1+frac{3/a}}=8 eching

$$3 + \frac { 15 } { 2 + \frac { 4 } { 1 + \frac { 3 } { a } } } = 8$$

a uchun yechish

$$a=1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$3+\frac{15}{2+\frac{4}{\frac{a}{a}+\frac{3}{a}}}=8$$

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

$$3+\frac{15}{2+\frac{4}{\frac{a+3}{a}}}=8$$

a qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. 4 ni \frac{a+3}{a} ga bo'lish 4 ga k'paytirish \frac{a+3}{a} ga qaytarish.

$$3+\frac{15}{2+\frac{4a}{a+3}}=8$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{a+3}{a+3} marotabaga ko'paytirish.

$$3+\frac{15}{\frac{2\left(a+3\right)}{a+3}+\frac{4a}{a+3}}=8$$

\frac{2\left(a+3\right)}{a+3} va \frac{4a}{a+3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$3+\frac{15}{\frac{2\left(a+3\right)+4a}{a+3}}=8$$

2\left(a+3\right)+4a ichidagi ko‘paytirishlarni bajaring.

$$3+\frac{15}{\frac{2a+6+4a}{a+3}}=8$$

2a+6+4a kabi iboralarga o‘xshab birlashtiring.

$$3+\frac{15}{\frac{6a+6}{a+3}}=8$$

a qiymati -3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. 15 ni \frac{6a+6}{a+3} ga bo'lish 15 ga k'paytirish \frac{6a+6}{a+3} ga qaytarish.

$$3+\frac{15\left(a+3\right)}{6a+6}=8$$

\frac{15\left(a+3\right)}{6a+6} ichida hali faktorlanmagan ifodalarni faktorlang.

$$3+\frac{15\left(a+3\right)}{6\left(a+1\right)}=8$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$3+\frac{5\left(a+3\right)}{2\left(a+1\right)}=8$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 ni \frac{2\left(a+1\right)}{2\left(a+1\right)} marotabaga ko'paytirish.

$$\frac{3\times 2\left(a+1\right)}{2\left(a+1\right)}+\frac{5\left(a+3\right)}{2\left(a+1\right)}=8$$

\frac{3\times 2\left(a+1\right)}{2\left(a+1\right)} va \frac{5\left(a+3\right)}{2\left(a+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3\times 2\left(a+1\right)+5\left(a+3\right)}{2\left(a+1\right)}=8$$

3\times 2\left(a+1\right)+5\left(a+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{6a+6+5a+15}{2\left(a+1\right)}=8$$

6a+6+5a+15 kabi iboralarga o‘xshab birlashtiring.

$$\frac{11a+21}{2\left(a+1\right)}=8$$

2 ga a+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{11a+21}{2a+2}=8$$

a qiymati -1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(a+1\right) ga ko'paytirish.

$$11a+21=16\left(a+1\right)$$

16 ga a+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$11a+21=16a+16$$

Ikkala tarafdan 16a ni ayirish.

$$11a+21-16a=16$$

-5a ni olish uchun 11a va -16a ni birlashtirish.

$$-5a+21=16$$

Ikkala tarafdan 21 ni ayirish.

$$-5a=16-21$$

-5 olish uchun 16 dan 21 ni ayirish.

$$-5a=-5$$

Ikki tarafini -5 ga bo‘ling.

$$a=\frac{-5}{-5}$$

1 ni olish uchun -5 ni -5 ga bo‘ling.

$$a=1$$