\(a,\dfrac{x-3}{2}+\dfrac{x+3}{3}+\dfrac{x+4}{4}=\dfrac{7}{6}\)
\(\Leftrightarrow\dfrac{12\left(x-3\right)}{24}+\dfrac{8\left(x+3\right)}{24}+\dfrac{6\left(x+4\right)}{24}=\dfrac{28}{24}\)
\(\Leftrightarrow12\left(x-3\right)+8\left(x+3\right)+6\left(x+4\right)=28\)
\(\Leftrightarrow12x-36+8x+24+6x+24-28=0\)
\(\Leftrightarrow26x-16=0\)
\(\Leftrightarrow x=\dfrac{8}{13}\)
\(b,\dfrac{x-1}{5}-\dfrac{x+2}{14}=\dfrac{x+1}{21}\)
\(\Leftrightarrow\dfrac{42\left(x-1\right)}{210}-\dfrac{15\left(x+2\right)}{210}=\dfrac{10\left(x+1\right)}{210}\)
\(\Leftrightarrow42\left(x-1\right)-15\left(x+2\right)=10\left(x+1\right)\)
\(\Leftrightarrow42x-42-15x-30=10x+10\)
\(\Leftrightarrow27x-72-10x-10=0\)
\(\Leftrightarrow17x-82=0\)
\(\Leftrightarrow x=\dfrac{82}{17}\)
\(c,\dfrac{4x-1}{3}-\dfrac{x+2}{2}=\dfrac{11}{6}\)
\(\Leftrightarrow\dfrac{2\left(4x-1\right)}{6}-\dfrac{3\left(x+2\right)}{6}=\dfrac{11}{6}\)
\(\Leftrightarrow2\left(4x-1\right)-3\left(x+2\right)=11\)
\(\Leftrightarrow8x-2-3x-6-11=0\)
\(\Leftrightarrow5x-19=0\)
\(\Leftrightarrow x=\dfrac{19}{5}\)
a,
\(\dfrac{x-3}{2}+\dfrac{x+3}{3}+\dfrac{x-4}{4}=\dfrac{7}{6}\)
\(\Leftrightarrow\dfrac{x-3}{2}+\dfrac{x+3}{3}+\dfrac{x-4}{4}-\dfrac{7}{6}=0\)
\(\Leftrightarrow\dfrac{12\left(x-3\right)}{24}+\dfrac{8\left(x+3\right)}{24}+\dfrac{6\left(x-4\right)}{24}-\dfrac{28}{24}=0\)
\(\Leftrightarrow\dfrac{12x-36}{24}+\dfrac{8x+24}{24}+\dfrac{6x-24}{24}-\dfrac{28}{24}=0\)
\(\Leftrightarrow\dfrac{12x-36+8x+24+6x-24-28}{24}=0\)
\(\Leftrightarrow26x-64=0\)
\(\Leftrightarrow x=\dfrac{32}{13}\)
Vậy pt có tập nghiệm \(S\in\left\{\dfrac{32}{13}\right\}\)
b,
\(\dfrac{x-1}{5}-\dfrac{x+2}{14}=\dfrac{x+1}{21}\)
\(\Leftrightarrow\dfrac{x-1}{5}-\dfrac{x+2}{14}-\dfrac{x+1}{21}=0\)
\(\Leftrightarrow\dfrac{294\left(x-1\right)}{1470}-\dfrac{105\left(x+2\right)}{1470}-\dfrac{70\left(x+1\right)}{1470}=0\)
\(\Leftrightarrow\dfrac{294x-294}{1470}-\dfrac{105x+210}{1470}-\dfrac{70x+70}{1470}=0\)
\(\Leftrightarrow\dfrac{294x-294-105x-210-70x-70}{1470}=0\)
\(\Leftrightarrow294x-294-105x-210-70x-70=0\)
\(\Leftrightarrow119x-574=0\)
\(\Leftrightarrow x=\dfrac{82}{17}\)
Vậy pt có tập nghiệm \(S\in\left\{\dfrac{82}{17}\right\}\).
c,
\(\dfrac{4x-1}{3}-\dfrac{x+2}{2}=\dfrac{11}{6}\)
\(\Leftrightarrow\dfrac{4x-1}{3}-\dfrac{x+2}{2}-\dfrac{11}{6}=0\)
\(\Leftrightarrow\dfrac{4\left(4x-1\right)}{12}-\dfrac{6\left(x+2\right)}{12}-\dfrac{22}{12}=0\)
\(\Leftrightarrow\dfrac{16x-4}{12}-\dfrac{6x+12}{12}-\dfrac{22}{12}=0\)
\(\Leftrightarrow16x-4-6x-12-22=0\)
\(\Leftrightarrow10x-38=0\)
\(\Leftrightarrow x=\dfrac{19}{5}\)
Vậy pt có tập nghiệm \(S\in\left\{\dfrac{19}{5}\right\}\)
