a) \(\dfrac{x}{2}-\left(\dfrac{3x}{5}-\dfrac{13}{5}\right)=\left(\dfrac{7}{5}+\dfrac{7}{10}x\right)\)
\(\Rightarrow\dfrac{x}{2}-\dfrac{3x}{5}+\dfrac{13}{5}=\dfrac{7}{5}+\dfrac{7x}{10}\)
\(\Rightarrow\dfrac{x}{2}-\dfrac{3x}{5}-\dfrac{7x}{10}=\dfrac{7}{5}-\dfrac{13}{5}\)
\(\Rightarrow\dfrac{5x}{10}-\dfrac{6x}{10}-\dfrac{7x}{10}=-\dfrac{6}{5}\)
\(\Rightarrow\dfrac{5x-6x-7x}{10}=-\dfrac{6}{5}\)
\(\Rightarrow\dfrac{-8x}{10}=-\dfrac{6}{5}\)
\(\Rightarrow\dfrac{-4x}{5}=-\dfrac{6}{5}\)
\(\Rightarrow-4x=-6\)
\(\Rightarrow x=-6:\left(-4\right)\)
\(\Rightarrow x=\dfrac{3}{2}\)
b) \(\dfrac{13}{x-1}+\dfrac{5}{2x-2}=\dfrac{6}{3x-3}\left(x\ne1\right)\)
\(\Rightarrow\dfrac{13}{x-1}+\dfrac{5}{2\left(x-1\right)}-\dfrac{6}{3\left(x-1\right)}=0\)
\(\Rightarrow\dfrac{13}{x-1}+\dfrac{5}{2\left(x-1\right)}-\dfrac{2}{x-1}=0\)
\(\Rightarrow\dfrac{13.2}{2\left(x-1\right)}+\dfrac{5}{2\left(x-1\right)}-\dfrac{2.2}{2\left(x-1\right)}=0\)
\(\Rightarrow\dfrac{26}{2\left(x-1\right)}+\dfrac{5}{2\left(x-1\right)}-\dfrac{4}{2\left(x-1\right)}=0\)
\(\Rightarrow\dfrac{26+5-4}{2\left(x-1\right)}=0\)
\(\Rightarrow26+1=0\)
\(\Rightarrow27=0\left(vô.lý\right)\)
\(\Rightarrow x\in\varnothing\)
c) \(\dfrac{2x-3}{3}+\dfrac{-3}{2}=\dfrac{5-3x}{6}-\dfrac{1}{3}\)
\(\Rightarrow\dfrac{2x-3}{3}-\dfrac{3}{2}=\dfrac{5-3x}{6}-\dfrac{2}{6}\)
\(\Rightarrow\dfrac{2\left(2x-3\right)}{6}-\dfrac{9}{6}=\dfrac{5-3x-2}{6}\)
\(\Rightarrow\dfrac{2\left(2x-3\right)-9}{6}=\dfrac{-3x+3}{6}\)
\(\Rightarrow2\left(2x-3\right)-9=-3x+3\)
\(\Rightarrow4x-6-9=-3x+3\)
\(\Rightarrow4x-15=-3x+3\)
\(\Rightarrow4x+3x=15+3\)
\(\Rightarrow7x=18\)
\(\Rightarrow x=18:7\)
\(\Rightarrow x=\dfrac{18}{7}\)
d) \(\dfrac{2}{3x}-\dfrac{3}{12}=\dfrac{4}{5}-\left(\dfrac{7}{x}-2\right)\left(x\ne0\right)\)
\(\Rightarrow\dfrac{24}{36x}-\dfrac{9x}{36x}=\dfrac{4}{5}-\dfrac{7}{x}+2\)
\(\Rightarrow\dfrac{24-9x}{36x}=-\dfrac{7}{x}+\dfrac{14}{5}\)
\(\Rightarrow\dfrac{24-9x}{36x}=-\dfrac{35}{5x}+\dfrac{14x}{5x}\)
\(\Rightarrow\dfrac{24-9x}{36x}=\dfrac{-35+14x}{5x}\)
\(\Rightarrow5x\left(24-9x\right)=36x\left(-35+14x\right)\)
\(\Rightarrow120x-45x^2=-1260x+504x^2\)
\(\Rightarrow120x-45x^2+1260x-504x^2=0\)
\(\Rightarrow1380x-549x^2=0\)
\(\Rightarrow3x\left(460-183x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}3x=0\\460-183x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{460}{183}\end{matrix}\right.\)
Mà \(x\ne0\)
\(\Rightarrow x=\dfrac{460}{183}\)
