[tex]\displaystyle\bf\\\frac{9a+1,5m}{9a^{2} -1,5am} -\frac{9a-1,5m}{9a^{2}+1,5am } +\frac{36a}{9a^{2}-0,25m^{2} } =\\\\\\=\frac{3\cdot(3a+0,5m)}{3a\cdot(3a-0,5m)} -\frac{3\cdot(3a-0,5m)}{3a\cdot(3a+0,5m) } +\frac{36a}{(3a-0,5m)(3a+0,5m) } =\\\\\\= \frac{3a+0,5m}{a\cdot(3a-0,5m)} -\frac{3a-0,5m}{a\cdot(3a+0,5m) } +\frac{36a}{(3a-0,5m)(3a+0,5m) } =\\\\\\=\frac{(3a+0,5m)(3a+0,5m)-(3a-0,5m)(3a-0,5m)+36a\cdot a}{a(3a-0,5m)(3a+0,5m)} =[/tex]

[tex]\displaystyle\bf\\=\frac{9a^{2}+3am+0,25m^{2} -9a^{2} +3am -0,25m^{2} +36a^{2} }{a(3a-0,5m)(3a+0,5m)} =\\\\\\==\frac{36a^{2} +6am}{a(3a-0,5m)(3a+0,5m)} ==\frac{12a\cdot(3a+0,5m)}{a(3a-0,5m)(3a+0,5m)} =\\\\\\=\frac{12}{3a-0,5m}=\frac{12\cdot 2}{(3a-0,5m)\cdot 2} =\frac{24}{6a-m}\\\\\\\frac{24}{6a-m}=\frac{24}{6a-m} }[/tex]

Тождество доказано