1+1/3/1+frac{2{2-frac{1/2}}+2-frac{1/3}{1-frac{2}{1+frac{1}{2}}}}{7+frac{1}{1-frac{1}{1+frac{7}{6}}}} eching

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

Baholash

$$-\frac{1}{2}=-0,5$$

Yechim qadamlari

1 ni \frac{3}{3} kasrga o‘giring.

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

\frac{3}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

4 olish uchun 3 va 1'ni qo'shing.

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

2 ni \frac{4}{2} kasrga o‘giring.

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

\frac{4}{2} va \frac{1}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

3 olish uchun 4 dan 1 ni ayirish.

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

2 ni \frac{3}{2} ga bo'lish 2 ga k'paytirish \frac{3}{2} ga qaytarish.

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

2\times \frac{2}{3} ni yagona kasrga aylantiring.

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

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

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

1 ni \frac{3}{3} kasrga o‘giring.

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

\frac{3}{3} va \frac{4}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

7 olish uchun 3 va 4'ni qo'shing.

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

\frac{4}{3} ni \frac{7}{3} ga bo'lish \frac{4}{3} ga k'paytirish \frac{7}{3} ga qaytarish.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{3} ni \frac{3}{7} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala 3 ni qisqartiring.

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

2 ni \frac{6}{3} kasrga o‘giring.

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

\frac{6}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

5 olish uchun 6 dan 1 ni ayirish.

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

1 ni \frac{2}{2} kasrga o‘giring.

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

\frac{2}{2} va \frac{1}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

3 olish uchun 2 va 1'ni qo'shing.

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

2 ni \frac{3}{2} ga bo'lish 2 ga k'paytirish \frac{3}{2} ga qaytarish.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-2\times \frac{2}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

2\times \frac{2}{3} ni yagona kasrga aylantiring.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2\times 2}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

1 ni \frac{3}{3} kasrga o‘giring.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{\frac{3}{3}-\frac{4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

\frac{3}{3} va \frac{4}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{\frac{3-4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

-1 olish uchun 3 dan 4 ni ayirish.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{-\frac{1}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

\frac{5}{3} ni -\frac{1}{3} ga bo'lish \frac{5}{3} ga k'paytirish -\frac{1}{3} ga qaytarish.

$$\frac{\frac{4}{7}+\frac{5}{3}\left(-3\right)}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

\frac{5}{3}\left(-3\right) ni yagona kasrga aylantiring.

$$\frac{\frac{4}{7}+\frac{5\left(-3\right)}{3}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{-15}{3}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

-5 ni olish uchun -15 ni 3 ga bo‘ling.

$$\frac{\frac{4}{7}-5}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

5 ni \frac{35}{7} kasrga o‘giring.

$$\frac{\frac{4}{7}-\frac{35}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

\frac{4}{7} va \frac{35}{7} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{4-35}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

-31 olish uchun 4 dan 35 ni ayirish.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

1 ni \frac{6}{6} kasrga o‘giring.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{6}{6}+\frac{7}{6}}}}$$

\frac{6}{6} va \frac{7}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{6+7}{6}}}}$$

13 olish uchun 6 va 7'ni qo'shing.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{13}{6}}}}$$

1 ni \frac{13}{6} ga bo'lish 1 ga k'paytirish \frac{13}{6} ga qaytarish.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-1\times \frac{6}{13}}}$$

\frac{6}{13} hosil qilish uchun 1 va \frac{6}{13} ni ko'paytirish.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{6}{13}}}$$

1 ni \frac{13}{13} kasrga o‘giring.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{13}{13}-\frac{6}{13}}}$$

\frac{13}{13} va \frac{6}{13} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{13-6}{13}}}$$

7 olish uchun 13 dan 6 ni ayirish.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{7}{13}}}$$

1 ni \frac{7}{13} ga bo'lish 1 ga k'paytirish \frac{7}{13} ga qaytarish.

$$\frac{-\frac{31}{7}}{7+1\times \frac{13}{7}}$$

\frac{13}{7} hosil qilish uchun 1 va \frac{13}{7} ni ko'paytirish.

$$\frac{-\frac{31}{7}}{7+\frac{13}{7}}$$

7 ni \frac{49}{7} kasrga o‘giring.

$$\frac{-\frac{31}{7}}{\frac{49}{7}+\frac{13}{7}}$$

\frac{49}{7} va \frac{13}{7} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-\frac{31}{7}}{\frac{49+13}{7}}$$

62 olish uchun 49 va 13'ni qo'shing.

$$\frac{-\frac{31}{7}}{\frac{62}{7}}$$

-\frac{31}{7} ni \frac{62}{7} ga bo'lish -\frac{31}{7} ga k'paytirish \frac{62}{7} ga qaytarish.

$$-\frac{31}{7}\times \frac{7}{62}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{31}{7} ni \frac{7}{62} ga ko‘paytiring.

$$\frac{-31\times 7}{7\times 62}$$

Surat va maxrajdagi ikkala 7 ni qisqartiring.

$$\frac{-31}{62}$$

\frac{-31}{62} ulushini 31 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{1}{2}$$

Omil

$$-\frac{1}{2} = -0,5$$