2/3-3/2*(2/3-3/2)+frac{1}{3}*(frac{3}{2}-3)= eching

$$\frac { 2 } { 3 } - \frac { 3 } { 2 } \cdot ( \frac { 2 } { 3 } - \frac { 3 } { 2 } ) + \frac { 1 } { 3 } \cdot ( \frac { 3 } { 2 } - 3 ) =$$

Baholash

$$\frac{17}{12}\approx 1,416666667$$

Yechim qadamlari

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

$$\frac{2}{3}-\frac{3}{2}\left(\frac{4}{6}-\frac{9}{6}\right)+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

\frac{4}{6} va \frac{9}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2}{3}-\frac{3}{2}\times \frac{4-9}{6}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

-5 olish uchun 4 dan 9 ni ayirish.

$$\frac{2}{3}-\frac{3}{2}\left(-\frac{5}{6}\right)+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{2} ni -\frac{5}{6} ga ko‘paytiring.

$$\frac{2}{3}-\frac{3\left(-5\right)}{2\times 6}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

\frac{3\left(-5\right)}{2\times 6} kasridagi ko‘paytirishlarni bajaring.

$$\frac{2}{3}-\frac{-15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

\frac{-15}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{3}-\left(-\frac{5}{4}\right)+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

-\frac{5}{4} ning teskarisi \frac{5}{4} ga teng.

$$\frac{2}{3}+\frac{5}{4}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

3 va 4 ning eng kichik umumiy karralisi 12 ga teng. \frac{2}{3} va \frac{5}{4} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{8}{12}+\frac{15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

\frac{8}{12} va \frac{15}{12} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{8+15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

23 olish uchun 8 va 15'ni qo'shing.

$$\frac{23}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

3 ni \frac{6}{2} kasrga o‘giring.

$$\frac{23}{12}+\frac{1}{3}\left(\frac{3}{2}-\frac{6}{2}\right)$$

\frac{3}{2} va \frac{6}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{23}{12}+\frac{1}{3}\times \frac{3-6}{2}$$

-3 olish uchun 3 dan 6 ni ayirish.

$$\frac{23}{12}+\frac{1}{3}\left(-\frac{3}{2}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{3} ni -\frac{3}{2} ga ko‘paytiring.

$$\frac{23}{12}+\frac{1\left(-3\right)}{3\times 2}$$

\frac{1\left(-3\right)}{3\times 2} kasridagi ko‘paytirishlarni bajaring.

$$\frac{23}{12}+\frac{-3}{6}$$

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

$$\frac{23}{12}-\frac{1}{2}$$

12 va 2 ning eng kichik umumiy karralisi 12 ga teng. \frac{23}{12} va \frac{1}{2} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{23}{12}-\frac{6}{12}$$

\frac{23}{12} va \frac{6}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{23-6}{12}$$

17 olish uchun 23 dan 6 ni ayirish.

$$\frac{17}{12}$$

Omil

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1,4166666666666667$$