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\(\Leftrightarrow\frac{x-1}{117}+1+\frac{x-2}{118}+1+\frac{x-3}{119}=\frac{x-4}{120}+1+\frac{x-5}{121}+1+\frac{x-6}{122}+1\)
\(\Leftrightarrow\frac{x+116}{117}+\frac{x+116}{118}+\frac{x+116}{119}-\frac{x+116}{120}-\frac{x+116}{121}-\frac{x+116}{122}=0\)
\(\Leftrightarrow\left(x+116\right)\left(\frac{1}{117}+\frac{1}{118}+\frac{1}{119}-\frac{1}{120}-\frac{1}{121}-\frac{1}{122}\right)=0\)
\(\Leftrightarrow x+116=0\Leftrightarrow x=-116\)
\(\frac{x-1}{117}+\frac{x-2}{118}+\frac{x-3}{119}=\frac{x-4}{120}+\frac{x-5}{121}+\frac{x-6}{122}\)
\(\Leftrightarrow\frac{x-1}{117}+1+\frac{x-2}{118}+1+\frac{x-3}{119}+1=\frac{x-4}{120}+1+\frac{x-5}{121}+1+\frac{x-6}{122}+1\)
\(\Leftrightarrow\frac{x+116}{117}+\frac{x+116}{118}+\frac{x+116}{119}-\frac{x+116}{120}-\frac{x+116}{121}-\frac{x+116}{122}=0\)
\(\Leftrightarrow\left(x+116\right)\left(\frac{1}{117}+\frac{1}{118}+\frac{1}{119}-\frac{1}{120}-\frac{1}{121}-\frac{1}{122}\right)=0\)
Vì \(\frac{1}{117}+\frac{1}{118}+\frac{1}{119}-\frac{1}{120}-\frac{1}{121}-\frac{1}{122}\ne0\)
Nên x + 116 = 0
<=> x = -116
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Ta có:
\(\dfrac{-119}{117}=-1-\dfrac{2}{117}\)
\(\dfrac{-117}{115}=-1-\dfrac{2}{115}\)
Vì \(\dfrac{2}{117}\) < \(\dfrac{2}{115}\) nên \(\dfrac{-119}{117}\) > \(\dfrac{-117}{115}\)
Vậy, \(\dfrac{-119}{117}\) > \(\dfrac{-117}{115}\)
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Đặt \(x=\frac{1}{117}\) và \(y=\frac{1}{119}\) ta có :
\(A=xy-4x\left(5+1-y\right)-\left(5+5xy\right)+\frac{8}{39}\)
\(A=xy-20x-4x+4xy-5-5xy+\frac{8}{39}\)
\(A=\left(xy+4xy-5xy\right)-\left(20x+4x\right)-\left(5-\frac{8}{39}\right)\)
Thay \(x=\frac{1}{117}\) ta được :
\(A=-24x-\frac{187}{39}\)
\(A=\frac{-24}{117}-\frac{561}{117}\)
\(A=\frac{-585}{117}\)
\(A=-5\)
Vậy \(A=-5\)
Chúc bạn học tốt ~
\(\frac{x+115}{15}+\frac{x+119}{19}=\frac{x+217}{117}+\frac{x+327}{227}\)
\(\Leftrightarrow\left(\frac{x+115}{15}-1\right)+\left(\frac{x+119}{19}-1\right)=\left(\frac{x+217}{117}-1\right)+\left(\frac{x+327}{227}-1\right)\)
\(\Leftrightarrow\frac{x+100}{15}+\frac{x+100}{19}=\frac{x+100}{117}+\frac{x+100}{227}\)
\(\Leftrightarrow\frac{x+100}{15}+\frac{x+100}{19}-\frac{x+100}{117}-\frac{x+100}{227}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{15}+\frac{1}{19}-\frac{1}{117}-\frac{1}{227}\right)=0\)
\(\Leftrightarrow x+100=0\)
\(\Leftrightarrow x=-100\)