[tex](\frac{3a}{1-3a}+\frac{2a}{1+3a}):\frac{6a^{2}+10a}{1-6+9a^{2}} =\\\\= \frac{3a(1+3a)+2a(1-3a)}{(1-3a)(1+3a)}\cdot\frac{9a^{2}-6a+1}{6a^{2}+10a} =\\\\=\frac{3a+9a^{2}+2a-6a^{2}}{(1-3a)(1+3a)}\cdot\frac{(3a-1)^{2}}{6a^{2}+10a} =\\\\=\frac{3a^{2}+5a}{(1-3a)(1+3a)}\cdot\frac{(3a-1)^{2}}{2a(3a+5)} =\\\\=\frac{a(3a-5)}{-(3a-1)(1+3a)}\cdot\frac{(3a-1)^{2}}{2a(3a+5)} =\\\\=\frac{(3a-1)^{2}}{-2(3a-1)(1+3a)} =\\\\= \frac{3a-1}{-2(1+3a)} =\\\\= \frac{1-3a}{2(1+3a)} =\\\\= \frac{1-3a}{2+6a}[/tex]
