Упростите выражение 5b/(b-3)-(b+6)/(2b-6)*90/(b^2+6b).

Ответ:

\[\frac{5b}{b - 3} - \frac{b + 6}{2b - 6} \cdot \frac{90}{b^{2} + 6b} =\]

\[= \frac{5b}{b - 3} - \frac{(b + 6) \cdot 90}{2 \cdot (b - 3) \cdot b(b + 6)} =\]

\[\mathbf{=}\frac{5b^{\backslash b}}{b - 3} - \frac{45}{b(b - 3)} = \frac{5b^{2} - 45}{b(b - 3)} =\]

\[= \frac{5 \cdot \left( b^{2} - 9 \right)}{b(b - 3)} = \frac{5 \cdot (b - 3)(b + 3)}{b(b - 3)} =\]

\[= \frac{5b + 15}{b}\]