x:(5/4+3/2-5/12)=6/7:(frac{4}{3}+frac{1}{2}-frac{1}{6}) eching

$$x : ( \frac { 5 } { 4 } + \frac { 3 } { 2 } - \frac { 5 } { 12 } ) = \frac { 6 } { 7 } : ( \frac { 4 } { 3 } + \frac { 1 } { 2 } - \frac { 1 } { 6 } )$$

x uchun yechish

$$x = \frac{6}{5} = 1\frac{1}{5} = 1,2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

4 va 2 ning eng kichik umumiy karralisi 4 ga teng. \frac{5}{4} va \frac{3}{2} ni 4 maxraj bilan kasrlarga aylantirib oling.

$$\frac{x}{\frac{5}{4}+\frac{6}{4}-\frac{5}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

\frac{5}{4} va \frac{6}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x}{\frac{5+6}{4}-\frac{5}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

11 olish uchun 5 va 6'ni qo'shing.

$$\frac{x}{\frac{11}{4}-\frac{5}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

4 va 12 ning eng kichik umumiy karralisi 12 ga teng. \frac{11}{4} va \frac{5}{12} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{x}{\frac{33}{12}-\frac{5}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

\frac{33}{12} va \frac{5}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x}{\frac{33-5}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

28 olish uchun 33 dan 5 ni ayirish.

$$\frac{x}{\frac{28}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

\frac{28}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

3 va 2 ning eng kichik umumiy karralisi 6 ga teng. \frac{4}{3} va \frac{1}{2} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{8}{6}+\frac{3}{6}-\frac{1}{6}}$$

\frac{8}{6} va \frac{3}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{8+3}{6}-\frac{1}{6}}$$

11 olish uchun 8 va 3'ni qo'shing.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{11}{6}-\frac{1}{6}}$$

\frac{11}{6} va \frac{1}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{11-1}{6}}$$

10 olish uchun 11 dan 1 ni ayirish.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{10}{6}}$$

\frac{10}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

\frac{6}{7} ni \frac{5}{3} ga bo'lish \frac{6}{7} ga k'paytirish \frac{5}{3} ga qaytarish.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{6}{7} ni \frac{3}{5} ga ko‘paytiring.

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

\frac{6\times 3}{7\times 5} kasridagi ko‘paytirishlarni bajaring.

$$\frac{x}{\frac{7}{3}}=\frac{18}{35}$$

Ikkala tarafini \frac{7}{3} ga ko‘paytiring.

$$x=\frac{18}{35}\times \frac{7}{3}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{18}{35} ni \frac{7}{3} ga ko‘paytiring.

$$x=\frac{18\times 7}{35\times 3}$$

\frac{18\times 7}{35\times 3} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{126}{105}$$

\frac{126}{105} ulushini 21 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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