If `(3x-5y)/(3x+5y) = 1/2`. Then find the value of `(3x^(2)-5y^(2))/(3x^(2) + 5y^(2))`.

Explanation

Given that `(3x - 5y)/(3x + 5y) = 1/2`
or , ` 6x - 10y = 3x + 5y`
or, ` 6x - 3x = 5y + 10y`
or, ` 3x = 15y`
or, ` x = (15y)/3 " or, " x = 5y`
`:. ` Given quantity ` = (3x^(2) - 5y^(2))/(3x^(2) + 5y^(2))`
` = (3 xx (5y)^(2) - 5y^(2))/(3 xx (5y)^(2) + 5y(2))`
` = (75y^(2) - 5y^(2))/(75y^(2) + 5y^(2)) = (70y^(2))/(80y^(2)) = 7/8`
Hence the required value = ` 7/8`.