Упростите выражение (a-15)/(4a-20)-(a-5)/(4a+20)+30/(a^2-25).

Ответ:

\[\frac{a - 15}{4a - 20} - \frac{a - 5}{4a + 20} + \frac{30}{a^{2} - 25} =\]

\[= \frac{a - 15^{\backslash a + 5}}{4(a - 5)} - \frac{a - 5^{\backslash a - 5}}{4(a + 5)} + \frac{30^{\backslash 4}}{(a - 5)(a + 5)} =\]

\[= \frac{a^{2} - 15a + 5a - 75 - a^{2} + 10a - 25 + 120}{4(a - 5)(a + 5)} =\]

\[= \frac{20}{4(a - 5)(a + 5)} = \frac{5}{a^{2} - 25}\]