If (a + b ) : (a - b) = 5 : 3, then find ( a 2 + b 2 ) : ( a 2 - b 2 ) .

(a + b) / (a - b) = 5/3
⇒ 3a + 3b = 5a - 5b
⇒ 2a = 8b
⇒ a = 4b,
⇒ a/b = 4/1
Now, ( a² + b² ) / (a² - b² ) = [a² / (b²+1)] / [a² / (b² -1)]
= [( a/b )² + 1] / [( a/b )² - 1] = [( 4/1 )² + 1] / [( 4/1 )² - 1]
= [16 + 1] / [16 - 1] = 17/15
∴ ( a² + b² ) : ( a² - b² ) = 17 : 15