Упростите выражение 3x/(x-5)-(x+3)/(6x-30)*450/(x^2+3x).

Ответ:

\[\frac{3x}{x - 5} - \frac{x + 3}{6x - 30} \cdot \frac{450}{x^{2} + 3x} =\]

\[= \frac{3x}{x - 5} - \frac{(x + 3) \cdot 450}{6(x - 5) \cdot x(x + 3)} =\]

\[= \frac{3x^{\backslash x}}{x - 5} - \frac{75}{x(x - 5)} = \frac{3x^{2} - 75}{x(x - 5)} =\]

\[= \frac{3 \cdot \left( x^{2} - 25 \right)}{x(x - 5)} = \frac{3(x - 5)(x + 5)}{x(x - 5)} =\]

\[= \frac{3x + 15}{x}\]