\(\dfrac{4x +2}{15x^3y}\) + \(\dfrac{5y-3}{9x^2y}\) + \(\dfrac{x +1}{5xy^3}\)
=\(\dfrac{\left(4x+2\right)\cdot3y^2}{45x^3y^3}\) + \(\dfrac{\left(5y-3\right)\cdot5xy^2}{45x^3y^3}\) + \(\dfrac{\left(x+1\right)\cdot9x^2}{45x^3y^3}\)
=\(\dfrac{12xy^2+6y^2+25xy^3-15xy^2+9x^3+9x^2}{45x^3y^3}\)
=\(\dfrac{9x^3+9x^2+25xy^3-3xy^2+6y^2}{45x^3y^3}\)