If $$\frac{x}{y} = \frac{3}{2}$$​, then find $$\frac{(x² + y²)} { (x² - y²)}.​$$​​

Given: 

​$$\frac{x}{y} = \frac{3}{2}$$ 

To find: $$\frac{(x² + y²)} { (x² - y²)}.​$$ 

Solution:​

Let x = 3k  and y = 2k 

Now, substituting the values in the expression;

​$$=\frac{(3k)^2 + (2k)^2}{(3k)^2 - (2k)^2} \\ \ \\ = \frac{9k^2 + 4k^2}{9k^2 - 4k^2} \\ \ \\ = \frac{13 \cancel {k^2}}{5\cancel{k^2}} \\ \ \\ =\bf \frac{13}{5}$$​​​​