a) \(\dfrac{4x-1}{3x^2y}-\dfrac{7x-1}{3x^2y}\)
\(=\dfrac{\left(4x-1\right)-\left(7x-1\right)}{3x^2y}\)
\(=\dfrac{4x-1-7x+1}{3x^2y}\)
\(=\dfrac{-3x}{3x^2y}\)
\(=\dfrac{-1}{xy}\)
b) \(\dfrac{4x+5}{2x-1}-\dfrac{5-9x}{2x-1}\)
\(=\dfrac{\left(4x+5\right)-\left(5-9x\right)}{2x-1}\)
\(=\dfrac{4x+5-5+9x}{2x-1}\)
\(=\dfrac{13x}{2x-1}\)
c) \(\dfrac{11x}{2x-3}-\dfrac{x-18}{3-2x}\)
\(=\dfrac{11x}{2x-3}+\dfrac{x-18}{2x-3}\)
\(=\dfrac{11x+\left(x-18\right)}{2x-3}\)
\(=\dfrac{11x+x-18}{2x-3}\)
\(=\dfrac{12x-18}{2x-3}\)
\(=\dfrac{6\left(2x-3\right)}{2x-3}\)
\(=\dfrac{6}{1}\)
\(=6\)
d) \(\dfrac{2x-7}{10x-4}-\dfrac{3x+5}{4-10x}\)
\(=\dfrac{2x-7}{10x-4}+\dfrac{3x+5}{10x-4}\)
\(=\dfrac{\left(2x-7\right)+\left(3x+5\right)}{10x-4}\)
\(=\dfrac{2x-7+3x+5}{10x-4}\)
\(=\dfrac{5x-2}{10x-4}\)
\(=\dfrac{5x-2}{2\left(5x-2\right)}\)
\(=\dfrac{1}{2}\)
