Simplify the following: \( \begin{array}{lll}\frac{x^{2}+2 x^{2}}{x+2 x} & \text { (2) } \frac{\left(3 x^{3}\right)^{2}}{3 x^{3}+3 x^{3}} & \text { (3) } \frac{2 x^{4}+8 x^{4}}{\left(5 x^{2}\right)\left(2 x^{2}\right)} \\ \frac{-x^{5}-2 x^{5}}{(-3 x)^{2}} & \text { (5) } \frac{-6 a^{9}+18 a^{9}}{-\left(-2 a^{2}\right)^{4}} & \text { (6) } \frac{-4 a^{2} b^{4}+a^{2} b^{4}}{3\left(2 a^{2} b\right)^{2}} \\ \text { G POLYNOMIALS BY MONOMIALS }\end{array} \)

Let's simplify each of the provided expressions step by step! 1) \( \frac{x^{2}+2 x^{2}}{x+2 x} = \frac{3x^{2}}{3x} = x \) 2) \( \frac{(3 x^{3})^{2}}{3 x^{3}+3 x^{3}} = \frac{9x^{6}}{6x^{3}} = \frac{3x^{6}}{2x^{3}} = \frac{3x^{3}}{2} \) 3) \( \frac{2 x^{4}+8 x^{4}}{(5 x^{2})(2 x^{2})} = \frac{10 x^{4}}{10 x^{4}} = 1 \) 4) \( \frac{-x^{5}-2 x^{5}}{(-3 x)^{2}} = \frac{-3x^{5}}{9x^{2}} = \frac{-x^{3}}{3} \) 5) \( \frac{-6 a^{9}+18 a^{9}}{-(-2 a^{2})^{4}} = \frac{12a^{9}}{16a^{8}} = \frac{3a}{4} \) 6) \( \frac{-4 a^{2} b^{4}+a^{2} b^{4}}{3(2 a^{2} b)^{2}} = \frac{-3 a^{2} b^{4}}{12 a^{4} b^{2}} = \frac{-b^{2}}{4 a^{2}} \) So, the final simplified expressions are: 1) \( x \) 2) \( \frac{3x^{3}}{2} \) 3) \( 1 \) 4) \( \frac{-x^{3}}{3} \) 5) \( \frac{3a}{4} \) 6) \( \frac{-b^{2}}{4a^{2}} \)