sqrt{4/3+1/9-1/12}:x=(1/3+frac{1}{2}):sqrt{(frac{1}{9}+frac{4}{3}*frac{3}{5}-frac{4}{15}):frac{29}{5}} eching

$$\sqrt { \frac { 4 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 12 } } : x = ( \frac { 1 } { 3 } + \frac { 1 } { 2 } ) : \sqrt { ( \frac { 1 } { 9 } + \frac { 4 } { 3 } \cdot \frac { 3 } { 5 } - \frac { 4 } { 15 } ) : \frac { 29 } { 5 } }$$

x uchun yechish

$$x=\frac{7}{15}\approx 0,466666667$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\sqrt{\frac{4}{3}+\frac{1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

3 va 9 ning eng kichik umumiy karralisi 9 ga teng. \frac{4}{3} va \frac{1}{9} ni 9 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{12}{9}+\frac{1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

\frac{12}{9} va \frac{1}{9} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{12+1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

13 olish uchun 12 va 1'ni qo'shing.

$$\sqrt{\frac{13}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

9 va 12 ning eng kichik umumiy karralisi 36 ga teng. \frac{13}{9} va \frac{1}{12} ni 36 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{52}{36}-\frac{3}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

\frac{52}{36} va \frac{3}{36} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{52-3}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

49 olish uchun 52 dan 3 ni ayirish.

$$\sqrt{\frac{49}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

\frac{49}{36} boʻlinmasining kvadrat ildizini \frac{\sqrt{49}}{\sqrt{36}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{7}{6}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

3 va 2 ning eng kichik umumiy karralisi 6 ga teng. \frac{1}{3} va \frac{1}{2} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{7}{6}=3x\left(\frac{2}{6}+\frac{3}{6}\right)$$

\frac{2}{6} va \frac{3}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

5 olish uchun 2 va 3'ni qo'shing.

$$\frac{7}{6}=3x\times \frac{5}{6}$$

3\times \frac{5}{6} ni yagona kasrga aylantiring.

$$\frac{7}{6}=\frac{3\times 5}{6}x$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$\frac{7}{6}=\frac{15}{6}x$$

\frac{15}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{7}{6}=\frac{5}{2}x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{5}{2}x=\frac{7}{6}$$

Ikki tarafini \frac{2}{5} va teskari kasri \frac{5}{2} ga ko‘paytiring.

$$x=\frac{7}{6}\times \frac{2}{5}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{6} ni \frac{2}{5} ga ko‘paytiring.

$$x=\frac{7\times 2}{6\times 5}$$

\frac{7\times 2}{6\times 5} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{14}{30}$$

\frac{14}{30} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{7}{15}$$