a: \(\frac{5}{6x^2y}+\frac{7}{12xy^2}+\frac{11}{18xy}\)
\(=\frac{5\cdot6\cdot y}{6x^2y\cdot6y}+\frac{7\cdot3\cdot x}{12xy^2\cdot3x}+\frac{11\cdot2xy}{18xy\cdot2xy}\)
\(=\frac{30y+21x+22xy}{36x^2y^2}\)
c: \(\frac{3}{2x}+\frac{3x-3}{2x-1}+\frac{2x^2+1}{4x^2-2x}\)
\(=\frac{3\left(2x-1\right)+2x\left(3x-3\right)+2x^2+1}{2x\left(2x-1\right)}\)
\(=\frac{6x-3+6x^2-6x+2x^2+1}{2x\left(2x-1\right)}=\frac{8x^2-2}{2x\left(2x-1\right)}=\frac{2\left(4x^2-1\right)}{2x\left(2x-1\right)}\)
\(\) \(=\frac{4x^2-1}{x\left(2x-1\right)}=\frac{2x+1}{x}\)
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