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\(\frac{4^{1007}.9^{1007}}{3^{2015}.16^{503}}=\frac{4^{1007}.\left(3^2\right)^{1007}}{3^{2015}.\left(4^2\right)^{503}}=\frac{4^{1007}.3^{2014}}{3^{2015}.4^{1006}}=\frac{4}{3}\)
a) \(\frac{3}{4}-\frac{2}{5}.x=x\)
\(\Rightarrow\frac{-2}{5}.x-x=\frac{-3}{4}\)
\(x.\left(\frac{-2}{5}-1\right)=\frac{-3}{4}\)
\(x.\frac{-7}{5}=\frac{-3}{4}\)
\(x=\frac{-3}{4}:\left(\frac{-7}{5}\right)\)
\(x=\frac{15}{28}\)
b) (2x-1).(3x-1/5).(4-2x) = 0
=> 2x - 1 = 0 => 2x = 1 => x = 1/2
3x-1/5 = 0 => 3x = 1/5 => x = 1/15
4-2x = 0 => 2x = 4 => x = 2
KL: x = 1/2 hoặc x = 1/15 hoặc x = 2
\(\frac{x+2}{2017}+\frac{x+3}{2016}+\frac{x+4}{2015}+\frac{x+5}{1007}+\frac{x+2074}{11}=0\)
\(\Leftrightarrow\frac{x+2}{2017}+1+\frac{x+3}{2016}+1+\frac{x+4}{2015}+1+\frac{x+5}{1007}+2+\frac{x+2074}{11}-5=0\)
\(\Leftrightarrow\frac{x+2019}{2017}+\frac{x+2019}{2016}+\frac{x+2019}{2015}+\frac{x+2019}{1007}+\frac{x+2019}{11}=0\)
\(\Leftrightarrow\left(x+2019\right)\left(\frac{1}{2017}+\frac{1}{2016}+\frac{1}{2015}+\frac{1}{1007}+\frac{1}{11}\right)=0\)
\(\Leftrightarrow\left(x+2019\right)=0vì\left(\frac{1}{2017}+\frac{1}{2016}+\frac{1}{2015}+\frac{1}{1007}+\frac{1}{11}\right)\ne0\)
\(\Leftrightarrow x=-2019\)
Bài giải
\(\frac{2-x}{2015}+\frac{3-x}{1007}+\frac{4-x}{671}=\frac{2005-x}{2}\)
\(( \frac{2-x}{2015}+1 )+ (\frac{3-x}{1007}+2 )+ ( \frac{4-x}{671}+3 )=\frac{2005-x}{2}+6\)
\(\frac{2017-x}{2015}+\frac{2017-x}{1007}+\frac{2017-x}{671}=\frac{2017-x}{2}\)
\(\frac{2017-x}{2015}+\frac{2017-x}{1007}+\frac{2017-x}{671}-\frac{2017-x}{2}=0\)
\((2017-x)(\frac{1}{2015}+\frac{1}{1007}+\frac{1}{671}-\frac{1}{2})=0\)
Do \(\frac{1}{2015}+\frac{1}{1007}+\frac{1}{671}-\frac{1}{2}\ne0\)
\(\Rightarrow\text{ }2017-x=0\)
\(\Rightarrow\text{ }x=2017\)
\(\frac{4^{1007}.9^{1007}}{3^{2015}.2^{2016}}=\frac{\left(2^2\right)^{1007}.\left(3^2\right)^{1007}}{3^{2015}.2^{2016}}\)
\(=\frac{2^{2014}.3^{2014}}{3^{2015}.2^{2016}}=\frac{2^{2014}.3^{2014}}{3^{2014}.2^{2014}.3.2^2}\)
\(=\frac{1}{3.2^2}=\frac{1}{3.4}=\frac{1}{12}\)
Rút gọn
\(\frac{4^{1007}\cdot9^{1007}}{3^{2015}\cdot2^{2016}}=\frac{\left(2^2\right)^{2007}\cdot\left(3^2\right)^{1007}}{3^{2015}\cdot2^{2016}}\)
\(=\frac{2^{2\cdot1007}\cdot3^{2\cdot1007}}{3^{2015}\cdot2^{2016}}=\frac{2^{2014}\cdot3^{2014}}{3^{2015}\cdot2^{2016}}\)
\(=\frac{1}{3.2^2}=\frac{1}{12}\)
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