If x: y=3: 2, then the ratio (2 x²+3 y²): (3 x²-2 y²) is equal to · ABC26GN3007

$$\begin{aligned} & \frac{x}{y}=\frac{3}{2} \Rightarrow \frac{x^{2}}{y^{2}}=\frac{9}{4} \Rightarrow \frac{2 x^{2}+3 y^{2}}{3 x^{2}-2 y^{2}} \\ & \quad=\frac{2\left(\frac{x^{2}}{y^{2}}\right)+3}{3\left(\frac{x^{2}}{y^{2}}\right)-2}=\frac{2 \times \frac{9}{4}+3}{3 \times \frac{9}{4}-2}=\frac{15}{2} \times \frac{4}{19}=\frac{30}{19} \\ & \Rightarrow\left(2 x^{2}+3 y^{2}\right):\left(3 x^{2}-2 y^{2}\right)=30: 19 . \end{aligned}$$