3.1. Simplify the following \( 3.1 .1 \frac{12 x y}{6} \times \frac{-2}{3 x^{2} y} \) \( 3.1 .2 \frac{2 a^{2} b}{3 a b}+\frac{6 a^{2} b^{2}}{4 a b} \)

To simplify \( \frac{12xy}{6} \times \frac{-2}{3x^{2}y} \), start by simplifying each fraction. The first fraction becomes \( 2xy \) after dividing \( 12xy \) by \( 6 \). The second fraction simplifies to \( -\frac{2}{3x^{2}y} \). Now, multiply: \[ 2xy \times \left(-\frac{2}{3x^{2}y}\right) = -\frac{4}{3x} \] For the second expression, simplifying \( \frac{2a^{2}b}{3ab} \) gives \( \frac{2a}{3} \), and simplifying \( \frac{6a^{2}b^{2}}{4ab} \) gives \( \frac{3ab}{2} \). Now, find a common denominator (which is \( 6 \)): \[ \frac{2a}{3} = \frac{4a}{6} \quad \text{and} \quad \frac{3ab}{2} = \frac{9ab}{6} \] Then, we combine them: \[ \frac{4a + 9ab}{6} \] So the final results are: 1. \( -\frac{4}{3x} \) 2. \( \frac{4a + 9ab}{6} \)