Упростите выражение 3/(2a-6)-(a+15)/(2a^2-18)-1/a.

Ответ:

\[\frac{3}{2a - 6} - \frac{a + 15}{2a^{2} - 18} - \frac{1}{a} =\]

\[= \frac{3^{\backslash a(a + 3)}}{2 \cdot (a - 3)} - \frac{a + 15^{\backslash a}}{2 \cdot \left( a^{2} - 9 \right)} - \frac{1^{\backslash 2(a^{2} - 9)}}{a} =\]

\[= \frac{3a^{2} + 9a - a^{2} - 15a - 2a^{2} + 18}{2a(a - 3)(a + 3)} =\]

\[= \frac{18 - 6a}{2a(a - 3)(a + 3)} = \frac{- 6(a - 3)}{2a(a - 3)(a + 3)} =\]

\[= \frac{- 3}{a(a + 3)}\]