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\(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{2}{7}:\frac{3}{5}+\frac{10}{9}\)
\(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{10}{21}+\frac{10}{9}\)
\(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{100}{63}\)
\(\frac{2}{3}:\frac{x}{5}\) \(=\frac{100}{63}-\frac{5}{7}\)
\(\frac{2}{3}:\frac{x}{5}\) \(=\frac{55}{63}\)
\(\frac{x}{5}\) \(=\frac{2}{3}:\frac{55}{63}\)
\(\frac{x}{5}\) \(=\frac{42}{55}\)
\(\frac{x\cdot11}{55}\) \(=\frac{42}{55}\)
\(\Rightarrow x\cdot11=42\)
\(x\) \(=42:11\)
\(x\) \(=\frac{42}{11}\)
\(\frac{1}{2}\times\frac{1}{3}\times.........\times\frac{1}{10}=\frac{1}{2\times3}+......+\frac{1}{9\times10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-..........-\frac{1}{10}=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
Kết quả nè bạn ơi;
A; 3/4 + 2/5=23/20
B;7/4 - 1/2=5/4
C;4/9 x 6/8=24/72
D;14/5 : 7/8=112/35
\(A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(\Leftrightarrow A=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
\(A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+\frac{4}{7.9.11}+\frac{4}{9.11.13}\)
\(\Rightarrow A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(\Rightarrow A=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
\(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{\left(2x+1\right)\cdot\left(2x+3\right)}\)
\(=\frac{1}{3}\left(\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+...+\frac{3}{\left(2x+1\right)\left(2x+3\right)}\right)\)
\(=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{\left(2x+1\right)}-\frac{1}{\left(2x+3\right)}\right)\)
\(=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{\left(2x+3\right)}\right)\)
\(=\frac{1}{3}\left(\frac{2x+3}{3\left(2x+3\right)}-\frac{3}{3\left(2x+3\right)}\right)\)
\(=\frac{1}{3}\left(\frac{2x+3-3}{3\left(2x+3\right)}\right)\)
\(=\frac{1}{3}\left(\frac{2x}{6x+9}\right)\)
\(=\frac{2x}{3\left(6x+9\right)}=\frac{2x}{18x+27}\)
a.7,2 :2 x 58,6 + 2,93 x 2 x 64
= 3,6 x 58,6 + 5,86 x 64
=210,96 + 357,04
=586
b.\(4\frac{2}{5}+2\frac{3}{7}-2\frac{2}{5}+5\frac{4}{7}\)
=\(\left(4\frac{2}{5}-2\frac{2}{5}\right)+\left(2\frac{3}{7}+5\frac{4}{7}\right)\)
= 2 + 8
= 10
c. 2 x 41 x 36 + 8 x 9 x 58 + 12 x 6
=72 x 41 + 72 x 58 + 72 x 1
=72 x ( 41 + 58 +1 )
=72 x 100
=7200
d, \(\frac{3}{5}\)x \(\frac{1}{2}\):\(\frac{2}{5}\)
=\(\frac{3}{5}\)x \(\frac{1}{2}\)x\(\frac{5}{2}\)
=\(\frac{3}{4}\)
\(\dfrac{3}{7}\): \(\dfrac{1}{3}\) + \(\dfrac{2}{7}\) \(\times\) \(\dfrac{1}{7}\)
= \(\dfrac{3}{7}\) \(\times\) \(\dfrac{3}{1}\) + \(\dfrac{2}{49}\)
= \(\dfrac{9}{7}\) + \(\dfrac{2}{49}\)
= \(\dfrac{63}{49}\) + \(\dfrac{2}{49}\)
= \(\dfrac{65}{49}\)