​$$\text{If } \frac{y}{x} = \frac{5}{6}, \text{ then } \frac{x^2 - y^2}{x^2 + y^2} = \underline{\phantom{------}}.$$​​​

Correct option is B

Given:

​$$\frac{y}{x} = \frac{5}{6}$$​​

Solution:

​$$\frac{x^2 - y^2}{x^2 + y^2}$$​​

=$$\frac{x^2 \left(1- \frac{y^2}{x^2}\right)}{x^2\left(1 + \frac{y^2}{x^2}\right)}$$​​

= $$\frac{\left(1- \frac{y^2}{x^2}\right)}{\left(1 + \frac{y^2}{x^2}\right)}$$​​

= $$\frac{\left(1- \frac{25}{36}\right)}{\left(1 + \frac{25}{36}\right)}$$​​

= $$\frac{\left( \frac{36-25}{36}\right)}{\left( \frac{36+25}{36}\right)}$$​​

= $$\frac{11}{61}$$​​