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Cách viết khác:
\(\dfrac{-8}{15}=\dfrac{-32}{60}=\dfrac{\left(-15\right)+\left(-12\right)+\left(-5\right)}{60}=\dfrac{-1}{4}+\dfrac{-1}{5}+\dfrac{-1}{12}.\)
\(1\frac{1}{30}:\left(24\frac{1}{6}-24\frac{1}{5}\right)-\frac{1\frac{1}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(-1\frac{1}{15}\right):\left(8\frac{1}{5}-8\frac{1}{3}\right)\)
\(\Rightarrow\frac{31}{30}:\left(\frac{145}{6}-\frac{121}{5}\right)-\frac{\frac{3}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{41}{5}-\frac{25}{3}\right)\)
\(\Rightarrow\frac{31}{30}:\left(\frac{725}{30}-\frac{726}{30}\right)-\frac{\frac{6}{4}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{123}{15}-\frac{125}{15}\right)\)
\(\Rightarrow\frac{31}{30}:\frac{-1}{30}-\frac{\frac{3}{4}}{4x-\frac{1}{2}}=\frac{-16}{15}:\frac{-2}{15}\)
\(\Rightarrow\frac{31}{30}.\frac{30}{-1}-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\frac{-16}{15}.\frac{15}{-2}\)
\(\Rightarrow\left(-31\right)-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=8\)
\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-31\right)-8\)
\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-39\right)\)
\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}:\left(-39\right)\)
\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}.\frac{-1}{39}\)
\(\Rightarrow4x-\frac{1}{2}=\frac{-1}{52}\)
\(\Rightarrow4x=\frac{-1}{52}+\frac{1}{2}\)
\(\Rightarrow4x=\frac{-1}{52}+\frac{26}{52}\)
\(\Rightarrow4x=\frac{25}{52}\)
\(\Rightarrow x=\frac{25}{52}:4\)
\(\Rightarrow x=\frac{25}{52}.\frac{1}{4}\)
\(\Rightarrow x=\frac{25}{208}\)
Vậy \(x=\frac{25}{208}\)
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