Упростите выражение: (8a-3)/(a+5)-(40-27a)/(a^2+2a-15).

Ответ:

\[\frac{8a - 3}{a + 5} - \frac{40 - 27a}{a^{2} + 2a - 15} =\]

\[= \frac{8a - 3^{\backslash a - 3}}{a + 5} - \frac{40 - 27a}{(a + 5)(a - 3)} =\]

\[= \frac{8a^{2} - 3a - 24a + 9 - 40 + 27a}{(a + 5)(a - 3)} =\]

\[= \frac{8a^{2} - 31}{a^{2} + 2a - 15}\]

\[a^{2} + 2a - 15 = 0\]

\[a_{1} + a_{2} = - 2;\ \ \ \ a_{1} \cdot a_{2} = - 15\]

• \(a_{1} = - 5;\ \ \ a_{2} = 3.\)