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Ta có :
\(\frac{2015.2000-15}{2016.1999+1}\)
= \(\frac{2015.1999+2015-15}{2015.1999+1999+1}\)
= \(\frac{2015.1999+2000}{2015.1999+2000}\)
= 1
Vậy \(\frac{2015.2000-15}{2016.1999+1}=1\)
\(a;0,\left(35\right)=0,3\left(53\right)>0,353\)
\(b;2,1\left(14\right)< 2,15< 2,\left(15\right)< 2,1\left(5\right)\)
a) \(\frac{-18}{91}\) và \(\frac{-23}{114}\)
\(\frac{-18}{91}=\frac{-18.114}{91.114}=\frac{-2052}{\text{10374}}\)
\(\frac{-23}{114}=\frac{-23.91}{114.91}=\frac{\text{-2093}}{10374}\)
Ta có:
\(\frac{-2052}{10374}< \frac{-2093}{10374}\)
\(\Rightarrow\)\(\frac{-18}{91}< \frac{-23}{114}\)
b) \(\frac{-22}{35}\) và \(\frac{-103}{177}\)
\(\frac{-22}{35}=\frac{-22.177}{35.177}=\frac{\text{-3894}}{\text{6195}}\)
\(\frac{-103}{177}=\frac{-103.35}{177.35}=\frac{\text{-3605}}{6195}\)
Ta có:
\(\frac{-3894}{6195}< \frac{-3605}{6195}\)
\(\Rightarrow\)\(\frac{-22}{35}< \frac{-103}{177}\)
Câu 1 :
\(a,2\left(\frac{3}{4}-5x\right)=\frac{4}{5}-3x\)
\(\Rightarrow\frac{3}{2}-10x=\frac{4}{5}-3x\)
\(\Rightarrow7x=\frac{3}{2}-\frac{4}{5}\)
\(\Rightarrow7x=\frac{7}{10}\)\(\Leftrightarrow x=0,1\)
\(b,\frac{3}{2}-4\left(\frac{1}{4}-x\right)=\frac{2}{3}-7x\)
\(\Rightarrow\frac{3}{2}-1+4x=\frac{2}{3}-7x\)
\(\Rightarrow11x=\frac{2}{3}+1-\frac{3}{2}\)
\(\Rightarrow11x=\frac{4+6-9}{6}-\frac{1}{6}\)
\(\Rightarrow x=\frac{1}{66}\)
Câu 2 :
\(a,\frac{2}{x-1}< 0\)
Vì \(2>0\Rightarrow\)để \(\frac{2}{x-1}< 0\)thì \(x-1< 0\Leftrightarrow x< 1\)
\(b,\frac{-5}{x-1}< 0\)
Vì \(-5< 0\)\(\Rightarrow\)để \(\frac{-5}{x-1}< 0\)thì \(x-1>0\Rightarrow x>1\)
\(c,\frac{7}{x-6}>0\)
Vì \(7>0\Rightarrow\)để \(\frac{7}{x-6}>0\)thì \(x-6>0\Rightarrow x>6\)
a)\(A>0\Leftrightarrow\left(a+3\right)\left(a-5\right)>0\Rightarrow\)có 2TH
TH1
nếu a + 3 < 0 => a < -3
TH2
nếu a - 5 > 0 => a > 5
b)\(A=0\Leftrightarrow a+3=0\Rightarrow a=-3\)
c) \(A< 0\Leftrightarrow\left(a+3\right)\left(a-5\right)< 0\Rightarrow\)có 2TH
TH1 8 > a + 3 > 0 => 5 > a > -3
TH2 2 < a - 5 < 0 => -3 < a < 5
d) \(A\in Z\Leftrightarrow a+3⋮a-5\)
\(\Rightarrow\left(a-5\right)+8⋮a-5\)
\(\Rightarrow a-5\inƯ\left(8\right)\)
\(\Rightarrow a-5\in\left\{1;2;4;8;-1;-2;-4;-8\right\}\)
\(\Rightarrow a\in\left\{6;7;9;13;4;3;1;-3\right\}\)