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\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
\(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)
\(=\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)+\frac{1}{3}\)
\(=\left(-1\right)+1+\frac{1}{3}\)
\(=\frac{1}{3}\)
\(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\\ =\left(\dfrac{103}{201}+\dfrac{13}{41}\right)-\dfrac{1363}{2747}\\ =\dfrac{6836}{8241}-\dfrac{1363}{2747}\\ =\dfrac{1}{3}\)
\(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\\ =\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}-\dfrac{79}{67}+\dfrac{28}{41}\\ =\dfrac{1}{3}+\left(\dfrac{12}{67}-\dfrac{79}{67}\right)+\left(\dfrac{13}{41}+\dfrac{28}{41}\right)\\ =\dfrac{1}{3}-\dfrac{67}{67}+\dfrac{41}{41}\\ =\dfrac{1}{3}-1+1\\ =\dfrac{1}{3}\)
\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\frac{79}{67}+\frac{28}{41}\) \(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}=\frac{1}{3}+\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)\) \(=\frac{1}{3}+\left(-1\right)+1=\frac{1}{3}\)
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\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
=\(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)
=\(\frac{1}{3}+\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)\)
=\(\frac{1}{3}+\left(\frac{-67}{67}\right)+\left(\frac{41}{41}\right)\)
=\(\frac{1}{3}-1+1\)
=\(\frac{1}{3}\)
\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
=\(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)
=\(\frac{1}{3}+\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)\)
=\(\frac{1}{3}+\left(\frac{-67}{67}\right)+\left(\frac{41}{41}\right)\)
=\(\frac{1}{3}-1+1\)
=\(\frac{1}{3}\)
\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
\(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}-\frac{28}{41}\)
\(=\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)+\frac{1}{3}\)
\(=\left(-1\right)+1+\frac{1}{3}\)
\(=0+\frac{1}{3}\)
\(=\frac{1}{3}\)
=1/3+12/67+13/41-79/67+28/41
=1/3+(12/67-79/67)+(13/41+28/41)
=1/3+(-1)+1
=1/3+0
=1/3
a, A = ( 1/3 + 12/67 + 13/41 ) - ( 79/67 - 28/41 )
A = (\(\frac13\) + \(\frac{12}{67}\) + \(\frac{13}{41}\)) - (\(\frac{79}{67}\) - \(\frac{28}{41}\))
A = \(\frac13\) + \(\frac{12}{67}\) + \(\frac{13}{41}\) - \(\frac{79}{67}\) + \(\frac{28}{41}\)
A = - (\(\frac{79}{67}-\frac{12}{67}\)) + (\(\frac{13}{41}\) + \(\frac{28}{41}\))
A = - 1 + 1 + \(\frac13\)
A = 0 + \(\frac13\)
A = \(\frac13\)
b, B = 3/4×7 + 3/7×10 + 3/10×13 + ......+ 3/73×76
B = \(\frac{3}{4\times7}\) + \(\frac{3}{7\times10}\) + \(\frac{3}{10\times13}\) + ... + \(\frac{3}{73\times76}\)
B = \(\frac14-\frac17\) + \(\frac17-\frac{1}{10}\) + ... + \(\frac{1}{73}-\frac{1}{76}\)
B = \(\frac14\) - \(\frac{1}{76}\)
B = \(\frac{19}{76}-\) \(\frac{1}{76}\)
B = \(\frac{18}{76}\)
B = \(\frac{9}{38}\)