a: \(\frac{3x-2}{2xy}-\frac{7x-4}{2xy}\)
\(=\frac{3x-2-7x+4}{2xy}=\frac{-4x+2}{2xy}=\frac{-2x+1}{xy}\)
b: \(\frac{9x+5}{2\left(x-1\right)}-\frac{5x-7}{2\left(x-1\right)}\)
\(=\frac{9x+5-5x+7}{2\left(x-1\right)}=\frac{4x+12}{2\left(x-1\right)}\)
\(=\frac{4\left(x+3\right)}{2\left(x-1\right)}=\frac{2\left(x+3\right)}{x-1}\)
c: \(\frac{x-1}{3x-4}-\frac{2x+3}{4-3x}\)
\(=\frac{x-1}{3x-4}+\frac{2x+3}{3x-4}\)
\(=\frac{x-1+2x+3}{3x-4}=\frac{3x+2}{3x-4}\)
d: \(\frac{1}{2x-1}-\frac{1}{1-4x^2}\)
\(=\frac{1}{2x-1}+\frac{1}{\left(2x-1\right)\left(2x+1\right)}\)
\(=\frac{2x+1+1}{\left(2x-1\right)\left(2x+1\right)}=\frac{2x+2}{4x^2-1}\)
e: \(\frac{1}{x-x^2}-\frac{x+5}{x-1}\)
\(=\frac{-1}{x\left(x-1\right)}-\frac{x+5}{x-1}\)
\(=\frac{-1-x\left(x+5\right)}{x\left(x-1\right)}=\frac{-1-x^2-5x}{x\left(x-1\right)}\)
f: \(\frac{2}{x^2-16}+\frac{1}{4-x}\)
\(=\frac{2}{\left(x-4\right)\left(x+4\right)}-\frac{1}{x-4}=\frac{2-\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}=\frac{-x-2}{\left(x-4\right)\left(x+4\right)}\)
