$\frac{x^3+9x^2}{2x}$ × $\frac{x^2-14x+45}{x^2-81}$
You asked:
Evaluate the expression: \(\frac{{x}^{3} + 9 \cdot {x}^{2}}{2 x} \cdot \frac{{x}^{2} - 14 x + 45}{{x}^{2} - 81}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{{x}^{3} + 9 \cdot {x}^{2}}{2 x} \cdot \frac{{x}^{2} - 14 x + 45}{{x}^{2} - 81} = \frac{\left(x^{3} + 9 x^{2}\right) \left(x^{2} - 14 x + 45\right)}{2 x \left(x^{2} - 81\right)} \)
Expanded
\[\frac{{x}^{3} + 9 \cdot {x}^{2}}{2 x} \cdot \frac{{x}^{2} - 14 x + 45}{{x}^{2} - 81} = \frac{x^{4}}{2 x^{2} - 162} - \frac{5 x^{3}}{2 x^{2} - 162} - \frac{81 x^{2}}{2 x^{2} - 162} + \frac{405 x}{2 x^{2} - 162}\]
Factored
\[\frac{{x}^{3} + 9 \cdot {x}^{2}}{2 x} \cdot \frac{{x}^{2} - 14 x + 45}{{x}^{2} - 81} = \frac{x \left(x - 5\right)}{2}\]