a) \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}=\left(\frac{-3}{7}+\frac{3}{7}\right)+\left(\frac{15}{26}-\frac{2}{13}\right)\)

\(=\frac{15-4}{26}=\frac{11}{26}\)

c) \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}=\frac{-11}{23}.\left(\frac{6}{7}+\frac{8}{7}\right)-\frac{1}{23}\)

\(=\frac{-11}{23}.2-\frac{1}{23}=\frac{-22-1}{23}=\frac{-23}{23}=-1\)

d) Đặt \(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}=A\)

Ta có: \(A.\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)=A.\left(\frac{4-3-1}{24}\right)=A.0=0\)

a. \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}=\frac{15}{13.2}-\frac{2}{13}=\frac{15}{13.2}-\frac{2.2}{13.2}=\frac{15-4}{26}=\frac{11}{26}\)

C. \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}=\frac{1}{23}.\left(-11.\frac{6}{7}-11.\frac{8}{7}-1\right)=\frac{1}{23}.\left(-22-1\right)=\frac{1}{23}.\left(-23\right)=-1\)

a.

\(-\frac{3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)\)

\(=-\frac{3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}\)

\(=\left(\frac{3}{7}-\frac{3}{7}\right)+\left(\frac{15}{26}-\frac{2}{13}\right)\)

\(=0+\left(\frac{15-4}{26}\right)\)

\(=\frac{11}{26}\)

c.

\(-\frac{11}{23}\times\frac{6}{7}+\frac{8}{7}\times\frac{-11}{23}-\frac{1}{23}\)

\(=-\frac{11}{23}\times\left(\frac{6}{7}+\frac{8}{7}\right)-\frac{1}{23}\)

\(=-\frac{11}{23}\times\frac{14}{7}\)

\(=-\frac{11}{23}\times2-\frac{1}{23}\)

\(=-\frac{22}{23}-\frac{1}{23}\)

\(=-\frac{23}{23}\)

\(=-1\)

d.

\(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right)\times\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)

\(=\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right)\times\left(\frac{4-3-1}{24}\right)\)

\(=\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right)\times\frac{0}{24}\)

\(=0\)

Chúc bạn học tốt

b)\(2\frac{17}{20}-1\frac{11}{5}+6\frac{9}{20}:3\)

= \(\frac{57}{20}-\frac{16}{5}+\frac{129}{20}\times\frac13\)

=\(\frac{57}{20}-\frac{16}{5}+\frac{129}{60}\)

=\(\frac{171}{60}-\frac{192}{60}+\frac{129}{60}\)

=\(\frac{108}{60}\)

=\(\frac95\)

c)\(4\frac37:\left(\frac75\times4\frac37\right)\)

=\(\frac{31}{7}:\left(\frac75\times\frac{31}{7}\right)\)

=\(\frac{31}{7}:\frac{31}{5}\)

=\(\frac{31}{7}\times\frac{5}{31}\)

=\(\frac57\)

d)\(\left(3\frac29\times\frac{15}{23}\times1\frac{7}{29}\right):\frac{5}{23}\)

=\(\left(\frac{29}{9}\times\frac{15}{23}\times\frac{36}{29}\right)\times\frac{23}{5}\)

=\(\left(\frac{29}{9}\times\frac{36}{29}\right)\times\left(\frac{15}{23}\times\frac{23}{5}\right)\)

=\(4\times\) \(3\)

=12

\(=\frac{6}{7}:\frac{-2}{26}+\frac{6}{7}:\frac{-3}{2}=\frac{-78}{7}+\frac{-4}{7}=\frac{-82}{7}\)

=\(\frac{6}{7}:\left(\frac{3}{26}_{ }-\frac{6}{26}\right)+\frac{6}{7}:\left(\frac{1}{10}-\frac{16}{10}\right)\)

=\(\frac{6}{7}:\frac{-3}{26}+\frac{6}{7}:\frac{-3}{10}\)

=\(\frac{6}{7}.\frac{-26}{3}+\frac{6}{7}.\frac{-10}{3}\)

=\(\frac{6}{7}.\left(\frac{-26}{3}+\frac{-10}{3}\right)\)

=\(\frac{6}{7}.\left(-12\right)\)

=\(\frac{-72}{7}=-10\frac{2}{7}\)

\(=\frac{-52}{7}+\frac{-4}{7}=-8\)

2: \(=\dfrac{0.8}{\dfrac{16}{25}-\dfrac{1}{25}}+\dfrac{\dfrac{71}{75}\cdot\dfrac{7}{4}}{\dfrac{119}{36}\cdot\dfrac{36}{17}}\)

\(=\dfrac{4}{5}\cdot\dfrac{5}{3}+\dfrac{71}{300}=\dfrac{471}{300}=\dfrac{157}{100}\)

3: \(=\dfrac{\dfrac{2}{5}-\dfrac{2}{9}+\dfrac{2}{11}}{\dfrac{7}{5}-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{2}{6}-\dfrac{2}{8}+\dfrac{2}{10}}{\dfrac{7}{6}-\dfrac{7}{8}+\dfrac{7}{10}}\)

=2/7-2/7=0

Ta có:

\(\left(\right. \frac{13 \frac{2}{9} - 15 \frac{2}{3}}{18 \frac{3}{7} - 17 \frac{1}{4}} \cdot \frac{30^{2} - 5^{4}}{25 - 12 \cdot 5^{2}} \left.\right) \cdot x = \frac{\frac{2}{11} + \frac{3}{13} + \frac{4}{15} + \frac{5}{17}}{4 \frac{1}{11} + \frac{5}{13} + \frac{9}{15} + \frac{13}{17}}\)

Bước 1: Đổi hỗn số về phân số

Bước 2: Tính toán từng phần

Ta có:

\(\frac{119}{9} - \frac{47}{3} = \frac{119 - 141}{9} = \frac{- 22}{9}\) \(\frac{129}{7} - \frac{69}{4} = \frac{516 - 483}{28} = \frac{33}{28}\) \(30^{2} - 5^{4} = 900 - 625 = 275\) \(25 - 12 \cdot 25 = 25 - 300 = - 275\)

Khi đó:

\(\left(\right. \frac{- 22}{9} \div \frac{33}{28} \cdot \frac{275}{- 275} \left.\right) = \left(\right. \frac{- 22}{9} \cdot \frac{28}{33} \cdot \left(\right. - 1 \left.\right) \left.\right) = \frac{616}{297}\)

Bước 3: Tính vế phải

Tử số:

\(\frac{2}{11} + \frac{3}{13} + \frac{4}{15} + \frac{5}{17} = \frac{35494}{36465}\)

Mẫu số:

\(4 \frac{1}{11} + \frac{5}{13} + \frac{9}{15} + \frac{13}{17} = \frac{149645}{36465}\)

→ Vế phải:

\(\frac{35494}{36465} \div \frac{149645}{36465} = \frac{35494}{149645}\)

Bước 4: Giải phương trình

\(\frac{616}{297} \cdot x = \frac{35494}{149645} \Rightarrow x = \frac{35494}{149645} \cdot \frac{297}{616} = \frac{813}{7118}\)

Vậy:

\(\boxed{x = \frac{813}{7118}}\)

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