[tex]\displaystyle\bf\\\frac{(4a+b)^{2} }{16a^{2} +b^{2} } +\frac{(4a-b)^{2} }{b^{2} +16a^{2} } =\frac{(4a+b)^{2}+(4a-b)^{2} }{16a^{2}+b^{2} } =\\\\\\=\frac{16a^{2} +8ab+b^{2} +16a^{2} -8ab+b ^{2}}{16a^{2} +b^{2} } =\frac{32a^{2} +2b^{2} }{16a^{2} +b^{2} } =\\\\\\=\frac{2\cdot(16a^{2} +b^{2} )}{16a^{2} +b^{2} } =2\\\\\\2=2[/tex]

Тождество доказано