If ` x/y = (a + 2)/(a - 2) `, then show that ` (x^(2) - y^(2))/(x^(2) + y^(2)) = (4a)/(a^(2) + 4)` .

Explanation

Given that ` x/y = (a+2)/(a - 2) " or, " x^(2)/y^(2) = ((a+2)^(2))/((a-2)^(2))` (Squaring)
or, `(x^(2)-y^(2))/(x^(2)+y^(2)) = ((a+2)^(2)-(a-2)^(2))/((a+2)^(2)+(a-2)^(2)) ` [Dividendo - componendo process .]
or, `(x^(2)-y^(2))/(x^(2)+y^(2)) = (4.a.2)/(2(a^(2)+2^(2))) " or, " (x^(2)-y^(2))/(x^(2)+y^(2)) = (4a)/(a^(2)+4)`
` :. (x^(2) -y^(2))/(x^(2) + y^(2)) = (4a)/(a^(2) + 4)`