\(\frac{4xy-5}{10x^3y}-\frac{6y^2-5}{10x^3y}=\frac{\left(4xy-5\right)-\left(6y^2-5\right)}{10x^3y}=\frac{4xy-6y^2}{10x^3y}=\frac{2y\left(2x-3y\right)}{2y.5x^3}=\frac{2x-3y}{5x^3}\)
\(\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10x-5}\)
\(=\frac{\left(2x+1\right)^2-\left(2x-1\right)^2}{\left(2x+1\right)\left(2x-1\right)}:\frac{4x}{10x-5}\)
\(=\frac{\left(2x+1+2x-1\right)\left(2x+1-2x+1\right)}{\left(2x+1\right)\left(2x-1\right)}\times\frac{10x-5}{4x}\)
\(=\frac{4x.2}{\left(2x+1\right)\left(2x-1\right)}\times\frac{5\left(2x-1\right)}{4x}\)
\(=\frac{10}{2x+1}\)
\(a,\frac{4xy-5}{10x^3y}-\frac{6y^2-5}{10x^3y}=\frac{\left(4xy-5\right)-\left(6y^2-5\right)}{10x^3y}=\frac{4xy-5-6y^2+5}{10x^3y}=\frac{4xy-6y^2}{10x^3y}\)
\(b,\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10x-5}\)
\(=\left(\frac{2x+1}{2x-1}+\frac{2x-1}{2x-1}\right):\frac{4x}{10x-5}\)
\(=\frac{2x+1+2x-1}{2x-1}:\frac{4x}{10x-5}\)
\(=\frac{4x}{2x-1}.\frac{10x-5}{4x}\)
\(=\frac{10x-5}{2x-1}\)
\(=\frac{5\left(2x-1\right)}{2x-1}\)
\(=\frac{5}{1}=5\)
