$\frac{3}{1 - a^2} + \frac{3}{1 + a^2} + \frac{6}{1 + a^4} + \frac{12}{1 + a^8} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{3(1 + a^2) + 3(1 - a^2)}{(1 - a^2)(1 + a^2)} + \frac{6}{1 + a^4} + \frac{12}{1 + a^8} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{3 + 3a^2 + 3 - 3a^2}{(1 - a^2)(1 + a^2)} + \frac{6}{1 + a^4} + \frac{12}{1 + a^8} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{6}{1 - a^4} + \frac{6}{1 + a^4} + \frac{12}{1 + a^8} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{6(1 + a^4) + 6(1 - a^4)}{(1 - a^4)(1 + a^4)} + \frac{12}{1 + a^8} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{6 + 6a^4 + 6 - 6a^4}{(1 - a^4)(1 + a^4)} + \frac{12}{1 + a^8} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{12}{1 - a^8} + \frac{12}{1 + a^8} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{12(1 + a^8) + 12(1 - a^8)}{(1 - a^8)(1 + a^8)} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{12 + 12a^8 + 12 - 12a^8}{(1 - a^8)(1 + a^8)} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{24}{1 - a^{16}} + \frac{24}{1 + a^{16}} = \frac{48}{1 - a^{32}}$
$\frac{24(1 + a^{16}) + 24(1 - a^{16})}{(1 - a^{16})(1 + a^{16})} = \frac{48}{1 - a^{32}}$
$\frac{24 + 24a^{16} + 24 - 24a^{16}}{(1 - a^{16})(1 + a^{16})} = \frac{48}{1 - a^{32}}$
$\frac{48}{1 - a^{32}} = \frac{48}{1 - a^{32}}$