a,\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\)
\(=\frac{3}{2x\left(x+1\right)}+\frac{2x-1}{\left(x-1\right)\left(x+1\right)}-\frac{2}{x}\)
\(=\frac{3\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}+\frac{\left(2x-1\right).2x}{2x\left(x-1\right)\left(x+1\right)}-\frac{2.2\left(x+1\right)\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{3x-3}{2x\left(x+1\right)\left(x-1\right)}+\frac{4x^2-2x}{2x\left(x-1\right)\left(x+1\right)}-\frac{4x^2-4}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{3x-3+4x^2-2x-4x^2+4}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{x+1}{2x\left(x+1\right)\left(x-1\right)}=\frac{1}{2x\left(x-1\right)}\)
\(b,\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
\(=\frac{3x}{5\left(x+y\right)}-\frac{x}{10\left(x-y\right)}\)
\(=\frac{3x.2\left(x-y\right)}{10\left(x+y\right).\left(x-y\right)}-\frac{x.\left(x+y\right)}{10\left(x-y\right).\left(x+y\right)}\)
\(=\frac{6x^2-6xy}{10\left(x+y\right)\left(x-y\right)}-\frac{x^2+xy}{10\left(x-y\right)\left(x+y\right)}\)
\(=\frac{6x^2-6xy-x^2+xy}{10\left(x+y\right)\left(x-y\right)}\)
\(=\frac{5x^2-5xy}{10\left(x+y\right)\left(x+y\right)}\)
\(=\frac{5x\left(x-y\right)}{10\left(x-y\right)\left(x+y\right)}=\frac{x}{2\left(x+y\right)}\)
