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

• \(13 \frac{2}{9} = \frac{119}{9}\),
• \(15 \frac{2}{3} = \frac{47}{3}\),
• \(18 \frac{3}{7} = \frac{129}{7}\),
• \(17 \frac{1}{4} = \frac{69}{4}\)

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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SORRY

1: \(\left(-\frac{25}{13}\right)+\left(-\frac{19}{17}\right)+\frac{12}{13}+\left(-\frac{25}{17}\right)\)

\(=\left(-\frac{25}{13}+\frac{12}{13}\right)+\left(-\frac{19}{17}-\frac{15}{17}\right)\)

\(=-\frac{13}{13}-\frac{34}{17}=-1-2=-3\)

2: \(\frac12-\left(-\frac13\right)+\frac{1}{23}+\frac16\)

\(=\left(\frac12+\frac13+\frac16\right)+\frac{1}{23}\)

\(=1+\frac{1}{23}=\frac{24}{23}\)

3: \(\left(-\frac37\right)\cdot\frac{5}{11}+\left(-\frac{5}{14}\right)\cdot\frac{5}{11}\)

\(=\frac{5}{11}\left(-\frac37-\frac{5}{14}\right)\)

\(=\frac{5}{11}\cdot\left(-\frac{6}{14}-\frac{5}{14}\right)=\frac{5}{11}\cdot\frac{-11}{14}=\frac{-5}{14}\)

4: \(\left(-\frac{5}{11}\right)\cdot\frac{7}{15}\cdot\frac{11}{-5}\cdot\left(-30\right)=-30\cdot\frac{7}{15}=-14\)

5: \(\left(-\frac59\right)\cdot\frac{3}{11}+\left(-\frac{13}{18}\right)\cdot\frac{3}{11}\)

\(=\frac{3}{11}\left(-\frac59-\frac{13}{18}\right)\)

\(=\frac{3}{11}\cdot\frac{-23}{18}=\frac{-23\cdot1}{11\cdot6}=-\frac{23}{66}\)

6: \(2\frac{2}{15}\cdot\frac{9}{17}\cdot\frac{3}{32}:\left(-\frac{3}{17}\right)\)

\(=\frac{32}{15}\cdot\frac{3}{32}\cdot\frac{9}{17}\cdot\frac{-17}{3}=\frac{3}{15}\cdot\frac{-9}{3}=\frac{-9}{15}=-\frac35\)

7: \(\left(-\frac34+\frac25\right):\frac37+\left(\frac35-\frac14\right):\frac37\)

\(=\left(-\frac34+\frac25+\frac35-\frac14\right):\frac37\)

\(=\left(-1+1\right):\frac37=0\)

8: \(\left(-\frac13\right)\cdot\left(-\frac{15}{19}\right)\cdot\frac{38}{45}=\frac{15}{45\cdot3}\cdot\frac{38}{19}=2\cdot\frac{1}{3\cdot3}=\frac29\)

9: \(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\cdots+\frac{1}{19\cdot20}\)

\(=\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{19}-\frac{1}{20}\)

\(=\frac12-\frac{1}{20}=\frac{9}{20}\)

10: \(\frac{1}{9\cdot10}-\frac{1}{8\cdot9}-\frac{1}{7\cdot8}-\cdots-\frac{1}{2\cdot3}-\frac{1}{1\cdot2}\)

\(=\frac{1}{9\cdot10}-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\cdots+\frac{1}{8\cdot9}\right)\)

\(=\frac19-\frac{1}{10}-\left(1-\frac12+\frac12-\frac13+\cdots+\frac18-\frac19\right)\)

\(=\frac19-\frac{1}{10}-\left(1-\frac19\right)=\frac19-\frac{1}{10}-\frac89=-\frac79-\frac{1}{10}=\frac{-79}{90}\)

Bai 1: tính nhanh A) -5/9 + 3/5 - 3/9 + -2/5 B) -5/13 + (3/5 + 3/1 - 4/10) C) 5/17 - 9/15 - 2/-17 + -2/15 D) (1/9 - 9/17) + 3/6 - ( 12/17 - 1/2) + -1/9 Bài 5: tính tổng A) 1/3 + -1/4 + 1/5 + 1/-6 + -1/-7 + 1/6 + -1/5 + 1/4 + 1/3 B) 1/12 +1/2.3+1/3.4+..+1/99100 Giúp mình nhé nhanh

c: Ta có: \(-\dfrac{5}{13}-\left(\dfrac{3}{5}+\dfrac{3}{13}-\dfrac{4}{10}\right)\)

\(=\dfrac{-5}{13}-\dfrac{3}{5}-\dfrac{3}{13}+\dfrac{2}{5}\)

\(=\dfrac{-8}{13}-\dfrac{1}{5}\)

\(=\dfrac{-53}{65}\)

d: Ta có: \(\left(\dfrac{1}{9}-\dfrac{9}{17}\right)+\dfrac{3}{6}-\left(\dfrac{12}{17}-\dfrac{1}{2}\right)+\dfrac{5}{9}\)

\(=\dfrac{1}{9}-\dfrac{9}{17}+\dfrac{1}{2}-\dfrac{12}{17}+\dfrac{1}{2}+\dfrac{5}{9}\)

\(=\dfrac{2}{3}+1-\dfrac{21}{17}\)

\(=\dfrac{22}{51}\)

Bài 1:

A = \(\frac15\) + \(\frac{3}{17}\) - \(\frac43\) + (\(\frac45\) - \(\frac{3}{17}\) + \(\frac13\)) - \(\frac17\) + (- \(\frac{14}{30}\))

A = \(\frac15\) + \(\frac{3}{17}\) - \(\frac43\) + \(\frac45\) - \(\frac{3}{17}\) + \(\frac13\) - \(\frac17\) - \(\frac{14}{30}\)

A = (\(\frac15\) + \(\frac45\)) + (\(\frac{3}{17}\) - \(\frac{3}{17}\)) - (\(\frac43-\frac13\)) - \(\frac{30}{210}\) - \(\frac{98}{210}\)

A = 1 + 0 - 1 - (\(\frac{30}{210}+\frac{98}{210}\))

A = 1 - 1 - \(\frac{228}{210}\)

A = 0 - \(\frac{128}{210}\)

A = - \(\frac{64}{105}\)

Bài 2:

B= (\(\frac58\) - \(\frac{4}{12}\) + \(\frac32\)) - (\(\frac58\) + \(\frac{9}{13}\)) - (\(\frac{-3}{2}\)) + \(\frac{7}{-15}\)

B = \(\frac58\) - \(\frac{4}{12}\) + \(\frac32\) - \(\frac58\) - \(\frac{9}{13}\) + \(\frac32\) - \(\frac{7}{15}\)

B = (\(\frac58\) - \(\frac58\)) + (\(\frac32\) + \(\frac32\)) - (\(\frac13\) + \(\frac{9}{13}\) + \(\frac{7}{15}\))

B = 0 + 3 - (\(\frac{65}{195}\) + \(\frac{135}{195}\) + \(\frac{91}{195}\))

B = 3 - (\(\frac{200}{195}\) + \(\frac{91}{195}\))

B = 3 - \(\frac{97}{65}\)

B = \(\frac{195}{65}\) - \(\frac{97}{65}\)

B = \(\frac{98}{65}\)

\(\dfrac{4}{17}\)

\(a,\dfrac{3}{5}+\dfrac{1}{5}.\dfrac{-17}{9}=\dfrac{3}{5}-\dfrac{17}{45}=\dfrac{27}{45}-\dfrac{17}{45}=\dfrac{10}{45}=\dfrac{2}{9}\\ b,\left(-\dfrac{4}{15}-\dfrac{18}{19}\right)-\left(\dfrac{20}{19}+\dfrac{11}{15}\right)=-\dfrac{4}{15}-\dfrac{18}{19}-\dfrac{20}{19}-\dfrac{11}{15}=\left(-\dfrac{4}{15}-\dfrac{11}{15}\right)-\left(\dfrac{18}{19}+\dfrac{20}{19}\right)=-1-2=-3\)

\(a,=\dfrac{3}{5}+\left(-\dfrac{17}{45}\right)=\dfrac{2}{9}\)

\(b,=-\dfrac{4}{15}-\dfrac{18}{19}-\dfrac{20}{19}-\dfrac{11}{15}=-3\)

a.2/9
b.-3

a.2/9 b.(-3)