\(a.\frac{7x-3}{x-1}=\frac{3}{2}\)
\(\Leftrightarrow\frac{7x-3}{x-1}-\frac{3}{2}=0\)
\(\Leftrightarrow\frac{2\left(7x-3\right)}{2.\left(x-1\right)}-\frac{3\left(x-1\right)}{2\left(x-1\right)}=0\)
\(\Leftrightarrow\frac{14x-6-3x+3}{2\left(x-1\right)}=0\)
\(\Leftrightarrow11x-3=0\)
\(\Leftrightarrow x=\frac{3}{11}\)
\(b.\frac{2\left(3-7x\right)}{1+x}=\frac{1}{2}\)
\(\Leftrightarrow\frac{6-14x}{1+x}-\frac{1}{2}=0\)
\(\Leftrightarrow\frac{2\left(6-14x\right)}{2\left(1+x\right)}-\frac{1+x}{2\left(1+x\right)}=0\)
\(\Leftrightarrow\frac{12-28x-1-x}{2\left(1+x\right)}=0\)
\(\Leftrightarrow11-29x=0\)
\(\Leftrightarrow x=\frac{11}{29}\)
\(c.\frac{1}{x-2}+3=\frac{3-x}{x-2}\)
\(\Leftrightarrow\frac{1}{x-2}+\frac{3\left(x-2\right)}{x-2}-\frac{3-x}{x-2}=0\)
\(\Leftrightarrow\frac{1+3x-6-3+x}{x-2}=0\)
\(\Leftrightarrow4x-8=0\)
\(\Leftrightarrow x=2\)
\(d.\frac{x+5}{x-5}-\frac{x-5}{x+5}=\frac{20}{x^2-25}\)
\(\Leftrightarrow\frac{\left(x+5\right)^2}{x^2-25}-\frac{\left(x-5\right)^2}{x^2-25}-\frac{20}{x^2-25}=0\)
\(\Leftrightarrow\frac{x^2+10x+25-x^2+10x-25-20}{x^2-25}=0\)
\(\Leftrightarrow20x-20=0\)
\(\Leftrightarrow x=10\)
