a: \(\dfrac{x}{2}-\left(\dfrac{3x}{5}-\dfrac{13}{5}\right)=\left(\dfrac{7}{5}+\dfrac{7}{10}x\right)\)
=>\(\dfrac{x}{2}-\dfrac{3x}{5}+\dfrac{13}{5}=\dfrac{7}{5}+\dfrac{7}{10}x\)
=>\(\dfrac{-1}{10}x-\dfrac{7}{10}x=\dfrac{7}{5}-\dfrac{13}{5}\)
=>\(-\dfrac{4}{5}x=-\dfrac{6}{5}\)
=>\(x=\dfrac{6}{5}:\dfrac{4}{5}=\dfrac{6}{4}=\dfrac{3}{2}\)
b: \(\dfrac{13}{x-1}+\dfrac{5}{2x-2}=\dfrac{6}{3x-3}\)
=>\(\dfrac{78}{6\left(x-1\right)}+\dfrac{15}{6\left(x-1\right)}=\dfrac{12}{6\left(x-1\right)}\)
=>93=12(vô lý)
Vậy: Phương trình vô nghiệm
c: \(\dfrac{2x-3}{3}+\dfrac{-3}{2}=\dfrac{5-3x}{6}-\dfrac{1}{3}\)
=>\(\dfrac{2\left(2x-3\right)-9}{6}=\dfrac{5-3x}{6}-\dfrac{2}{6}\)
=>2(2x-3)-9=5-3x-2
=>4x-6-9=-3x+3
=>4x-15=-3x+3
=>7x=18
=>\(x=\dfrac{18}{7}\)
d: \(\dfrac{2}{3x}-\dfrac{3}{12}=\dfrac{4}{5}-\left(\dfrac{7}{x}-2\right)\)
=>\(\dfrac{2}{3x}-\dfrac{1}{4}=\dfrac{4}{5}-\dfrac{7}{x}+2\)
=>\(\dfrac{2}{3x}+\dfrac{7}{x}=\dfrac{4}{5}+2+\dfrac{1}{4}\)
=>\(\dfrac{2}{3x}+\dfrac{21}{3x}=\dfrac{16}{20}+\dfrac{40}{20}+\dfrac{5}{20}=\dfrac{61}{20}\)
=>\(\dfrac{23}{2x}=\dfrac{61}{20}\)
=>\(2x=20\cdot\dfrac{23}{61}\)
=>\(x=10\cdot\dfrac{23}{61}=\dfrac{230}{61}\left(nhận\right)\)
