Mixed operations with algebraic fractions

Express each of the following as a single fraction in its simplest form.

1. \(\frac{(-3a^2bc^2)^2}{18abc}\times\frac{12a^3b^2}{(-2abc)^3}\)
2. \(\frac{3a^2b^3}{14xc^2}\times\frac{7x}{9ab}\div\frac{2ab^2}{3c}\)
3. \((\frac{4xy}{5})^2\div\frac{8xy}{15}+\frac{2xy}{3}\)
4. \(\frac{6a^2-3ab-9b^2}{2a-3b+12mb-8ma}\)
5. \(\frac{(x+3y)^2-25y^2}{x^2-4y^2}\)
6. \((\frac1{a^2}-\frac1a)\div(\frac1{a^3}-\frac1{a^2})\)