Упростите выражение (8a^3+100a)/(a^3+125)-(4a^2)/(a^2-5a+25).

Ответ:

\[\frac{8a^{3} + 100a}{a^{3} + 125} - \frac{4a^{2}}{a^{2} - 5a + 25} =\]

\[= \frac{8a^{3} + 100a}{(a + 5)\left( a^{2} - 5a + 25 \right)} - \frac{4{a^{2}}^{\backslash a + 5}}{a^{2} - 5a + 25} =\]

\[= \frac{8a^{3} + 100a - 4a^{3} - 20a^{2}}{(a + 5)\left( a^{2} - 5a + 25 \right)} =\]

\[= \frac{4a^{3} - 20a^{2} + 100a}{(a + 5)\left( a^{2} - 5a + 25 \right)} =\]

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