a: \(=\dfrac{5\cdot5\cdot y^2}{10x^2y^3}+\dfrac{3\cdot2x\cdot y+x\cdot10x^2}{10x^2y^3}\)
\(=\dfrac{25y^2+10x^3+6xy}{10x^2y^3}\)
b: \(=\dfrac{x^2+x+\left(2x+3\right)\cdot2}{2x\left(x+3\right)}\)
\(=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}=\dfrac{\left(x+2\right)\left(x+3\right)}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)
c: \(\dfrac{3x+5}{x^2-5x}+\dfrac{25-x}{25-5x}\)
\(=\dfrac{3x+5}{x\left(x-5\right)}+\dfrac{x-25}{5\left(x-5\right)}\)
\(=\dfrac{15x+25+x^2-25x}{5x\left(x-5\right)}=\dfrac{x^2-10x+25}{5x\left(x-5\right)}=\dfrac{x-5}{5x}\)
d: \(=\dfrac{x^2-x^4+x^4+1+1-x^2}{1-x^2}=\dfrac{2}{1-x^2}\)
e: \(=\dfrac{4x^2-3x+17+\left(2x-1\right)\left(x-1\right)-6x^2-6x-6}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{-2x^2-9x+11+2x^2-3x+1}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{-12\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{-12}{x^2+x+1}\)
