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\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2008}{2010}\)
\(\Leftrightarrow2\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{\left(x+1\right)-x}{x\left(x+1\right)}\right)=\frac{2008}{2010}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2008}{2010}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1004}{2010}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2010}\)
\(\Leftrightarrow x+1=2010\)
\(\Leftrightarrow x=2009\)
1/4+2/5+6/8+2/15+6/7
=(1/4+6/8)+(2/5+2/15)+6/7
=(2/8+6/8)+(6/15+2/15)+6/7
=1+8/15+6/7
=1+56/105+90/105
=1+146/105
=1+105/105+41/105
=1+1+41/105
=2+41/105
=2 và 41/105
2 và 41/105 là hỗn số nha
1/4+2/5+6/8+2/15+6/7
Ta có:
1/4=1-3/4
6/8=3/4
2/15=2/3*5=1/3-1/5
==> 1-3/4+2/5+3/4+1/3-1/5+6/7
=1+1/3+1/5+6/7
=(105+35+21+90)/105
=251/105.
\(0,5.1\frac{1}{3}.75\%:\frac{2}{5}+\frac{3}{5}\)
\(=\frac{1}{2}.\frac{4}{3}.\frac{3}{4}:\frac{2}{5}+\frac{3}{5}\)
\(=\frac{1}{2}.\frac{4}{3}.\frac{3}{4}.\frac{5}{2}+\frac{3}{5}\)
\(=\frac{5}{4}+\frac{3}{5}\)
\(=\frac{37}{20}\)
\(0,5.1\frac{1}{3}.75\%:\frac{2}{5}+\frac{3}{5}\)
\(=\frac{1}{2}.\frac{4}{3}.\frac{3}{4}:\frac{2}{5}+\frac{3}{5}\)
\(=\frac{1}{2}.\frac{4}{3}.\frac{3}{4}.\frac{5}{2}+\frac{3}{5}\)
\(=\frac{1.4.3.5}{2.3.4.2}+\frac{3}{5}\)
\(=\frac{5}{4}+\frac{3}{5}\)
\(=\frac{37}{20}\)
~Học tốt~
Ta có: 75%.x + \(\frac{1}{5}\).x = \(\frac{1}{6}\)
\(\frac{3}{4}\cdot x+\frac{1}{5}\cdot x=\frac{1}{6}\)
\(x\left(\frac{3}{4}+\frac{1}{5}\right)=\frac{1}{6}\)
\(\frac{19}{20}x=\frac{1}{6}\)
\(x=\frac{1}{6}:\frac{19}{20}=\frac{10}{57}\)
tích nha
75%.x+1/5.x=1/6 3/4.x+1/5.x=1/6 x.(3/4+1/5)=1/6 : x.19/20=1/6 suy ra x=1/6:19/20=1/6.20/19=10/57