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\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{42}{43}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}+\frac{42}{43}\)
\(=6-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)+\frac{42}{43}\)
\(=6-\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\right)+\frac{42}{43}\)
\(=6-\left(1-\frac{1}{6}\right)+\frac{42}{43}\)
...
bn tự tính tiếp nha
\(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{2}{7}:\frac{3}{5}+\frac{10}{9}\)
\(\Rightarrow\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{2}{7}.\frac{5}{3}+\frac{10}{9}\)
\(\Rightarrow\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{10}{21}+\frac{10}{9}\)
\(\Rightarrow\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{100}{63}\)
\(\Rightarrow\frac{2}{3}:\frac{x}{5}=\frac{100}{63}-\frac{5}{7}\)
\(\Rightarrow\frac{2}{3}:\frac{x}{5}=\frac{55}{63}\)
\(\Rightarrow\frac{x}{5}=\frac{2}{3}:\frac{55}{63}\)
\(\Rightarrow\frac{x}{5}=\frac{2}{3}.\frac{63}{55}\)
\(\Rightarrow\frac{x}{5}=\frac{42}{55}\)
\(\Rightarrow x=\frac{42.5}{55}=\frac{42}{11}\)
Nên ta chọn đáp án D là đáp án đúng!
( trong bài có dấu . tức là dấu dấu nhân bn nhé )
2/3 : x/5 + 5/7 = 2/7 : 3/5 + 10/9
2/3 : x/5 + 5/7 = 10/21 + 10/9
2/3 : x/5 + 5/7 = 100/63
2/3 : x/5 = 100/63 - 5/7
2/3 : x/5 = 55/63
2/3 . 5/x= 55/63
=) 5/x = 55/63 : 2/3
=) 5/x = 55/42
ta có : a/b = c/d =) a.d=b.c
(=) 55.x = 5.42
55.x = 210
=) x = 210 : 55 = 42/11
vậy đáp án đúng là D
chúc bn học tốt
(5/6+2/7-5/42)+(1/12+2/3+1/4)+1/25
=\(\frac{35+12-5}{42}+\frac{1+8+3}{12}\)+\(\frac{1}{25}\)
=1+1+\(\frac{1}{25}\)=\(2+\frac{1}{25}=\frac{50+1}{25}\)=\(\frac{51}{25}\)
\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}\)
\(=\frac{1+2}{1.2}-\frac{2+3}{2.3}+\frac{3+4}{3.4}-\frac{4+5}{4.5}+\frac{5+6}{5.6}-\frac{6+7}{6.7}+\frac{7+8}{7.8}-\frac{8+9}{8.9}+\frac{9+10}{9.10}\)
\(=1+\frac{1}{2}-\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-...-\frac{1}{8}-\frac{1}{9}+\frac{1}{9}+\frac{1}{10}\)
\(=\frac{11}{10}\)
=42* (3+12-5)
=42*4=168
42 x 3 + 42 x 12 - 42 x 5
= 42 x ( 3 + 12 - 5 )
= 42 x 10
= 420