If $$\frac{a}{b} = \frac{{25}}{6}{\text{,}}$$   then the value of $$\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$$   is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{a}{b} = \frac{{25}}{6} \cr & \frac{{{a^2}}}{{{b^2}}} = \frac{{{{25}^2}}}{{{6^2}}} \cr & \Rightarrow \frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}} \cr & \Rightarrow \frac{{{{25}^2} - {6^2}}}{{{{25}^2} + {6^2}}} \cr & \Rightarrow \frac{{625 - 36}}{{625 + 36}} \cr & \Rightarrow \frac{{589}}{{661}} \cr} $$