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(1-1/2)x(1-1/3)x(1-1/4)x....x(1-1/1996)x(1-1/997)
=1/2x2/3x3/4x....x1995/1996x1996/1997
=1x2x3x...x1995x1996/2x3x4x...x1996x1997
=1/1997
\(\Rightarrow\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{1996}{1997}\)
\(\Leftrightarrow1x\frac{1}{1997}\)\(=\frac{1}{1997}\)
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a) \(\dfrac{1997x1996-1}{1995x1997+1996}=\dfrac{1997x\left(1995+1\right)-1}{1995x1997+1996}\)
\(=\dfrac{1997x1995+1997-1}{1995x1997+1996}=\dfrac{1997x1995+1996}{1995x1997+1996}=1\)
b) \(\dfrac{1997x1996-995}{1995x1997+1002}=\dfrac{1997x\left(1995+1\right)-995}{1995x1997+1002}\)
\(=\dfrac{1997x1995+1997-995}{1995x1997+1002}=\dfrac{1997x1995+1002}{1995x1997+1002}=1\)
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mẫu số
:1997x1996-1
1997x(1995+1)-1
1997x1995+1997x1-1
1997x1995+1997-1
1997x1995+1996
->1997x1996-1/1995x1997+1996
l i k e nhé
Bạn Huy Hoàng làm đúng đó mình đã làm bài này rồi.Chúc bạn làm bài tốt.
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Bạn tham khảo theo đường link này nhé có 1 bài tương tự đó : https://olm.vn/hoi-dap/question/1042256.html
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\(\frac{1997\times1996-1}{1995\times1997+1996}=\frac{1997\times\left(1995+1\right)-1}{1995\times1997+1996}=\frac{1997\times1995+1997-1}{1995\times1997+1996}\)
\(=\frac{1997\times1995+1996}{1995\times1997+1996}=1\)
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\(\dfrac{1997\times1996-1}{1995\times1997+1996}\)
= \(\dfrac{1997\times\left(1995+1\right)-1}{1995\times1997+1996}\)
= \(\dfrac{1997\times1995+1997-1}{1995\times1997+1996}\)
= \(\dfrac{1995\times1997+1996}{1995\times1997+1996}\)
= 1
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a) \(\frac{35}{14}=\frac{5\times7}{2\times7}=\frac{5}{2}\)
\(\frac{125}{50}=\frac{5\times5\times5}{2\times5\times5}=\frac{5}{2}\)
b)\(\frac{4\times5+4\times11}{8\times7+4\times3}=\frac{4\times\left(5+11\right)}{4\times\left(2\times7+3\right)}=\frac{16}{17}\)
c) \(\frac{3\times11+7\times11}{22\times2+11\times6}=\frac{11\times\left(3+7\right)}{22\times\left(2+3\right)}=\frac{11\times10}{22\times5}=\frac{11\times2\times5}{11\times2\times5}=1\)
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\(\dfrac{1995x1997-1}{1996x1995+1994}=\dfrac{1995x\left(1996+1\right)-1}{1996x1995+1994}\)
\(=\dfrac{1995x1996+1995-1}{1996x1995+1994}=\dfrac{1995x1996+1994}{1996x1995+1994}=1\)
( 1 - 1/2 ) x ( 1 - 1/3 ) x ( 1 - 1/4 ) x .... x ( 1 - 1/1996 ) x ( 1 - 1/1997 )
= 1/2 x 2/3 x 3/4 x .... x 1995/1996 x 1996/1997
= 1 x 2 x 3 x 4 x .... x 1995 x 1996 / 2 x 3 x 4 x .... x 1996 x 1997
= 1/1997