Simplify the following expression: (5c^3 (c+d)^3)/(10c^5 (c+d)^2).
You asked:
Simplify the expression: \(\frac{5 \cdot {c}^{3} \cdot {\left( c + d \right)}^{3}}{10 \cdot {c}^{5} \cdot {\left( c + d \right)}^{2}}\)
MathBot Answer:
Simplified:
\[ \frac{5 \cdot {c}^{3} \cdot {\left( c + d \right)}^{3}}{10 \cdot {c}^{5} \cdot {\left( c + d \right)}^{2}} = \frac{c + d}{2 c^{2}} \]
Expanded:
\[ \frac{5 \cdot {c}^{3} \cdot {\left( c + d \right)}^{3}}{10 \cdot {c}^{5} \cdot {\left( c + d \right)}^{2}} = \frac{c^{3}}{2 c^{4} + 4 c^{3} d + 2 c^{2} d^{2}} + \frac{3 c^{2} d}{2 c^{4} + 4 c^{3} d + 2 c^{2} d^{2}} + \frac{3 d^{2} c}{2 c^{4} + 4 c^{3} d + 2 c^{2} d^{2}} + \frac{d^{3}}{2 c^{4} + 4 c^{3} d + 2 c^{2} d^{2}} \]