16/((-4 + m)^2 + 4 m^2) == 16/(64/5 + 5 (-(4/5) + m)^2)
Example1:For the equation above, how can we manipulate it to complete the square in the denominator of the left-hand fraction and obtain the right-hand side?
2 Sqrt[4 - 16/((-4 + m)^2 + 4 m^2)] ==
2 Sqrt[4 - 16/(64/5 + 5 (-(4/5) + m)^2)]
Example2:How can one complete the square in the denominator of the fractional expression inside the radical on the left-hand side so as to obtain the expression on the right-hand side?
(4 (12 - 8 m + 5 m^2))/(16 - 8 m + 5 m^2) == (
4 (44/5 + 5 (-(4/5) + m)^2))/(64/5 + 5 (-(4/5) + m)^2)
Example3:For the equation above, since both the numerator and the denominator of the left-hand expression can be completed-square, how can one simultaneously complete the square in both the numerator and the denominator to obtain the form shown on the right-hand side?
In other words, how can the left-hand expression be transformed into the completed-square form shown on the right-hand side using Mathematica code?
