$\frac{x}{8x+48}$ รท $\frac{x^2+11x+18}{x^2+8x+12}$
You asked:
Evaluate the expression: \(\frac{\frac{x}{8 x + 48}}{\frac{{x}^{2} + 11 x + 18}{{x}^{2} + 8 x + 12}}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{\frac{x}{8 x + 48}}{\frac{{x}^{2} + 11 x + 18}{{x}^{2} + 8 x + 12}} = \frac{x \left(x^{2} + 8 x + 12\right)}{\left(8 x + 48\right) \left(x^{2} + 11 x + 18\right)} \)
Expanded
\[\frac{\frac{x}{8 x + 48}}{\frac{{x}^{2} + 11 x + 18}{{x}^{2} + 8 x + 12}} = \frac{x}{\frac{8 x^{3}}{x^{2} + 8 x + 12} + \frac{136 x^{2}}{x^{2} + 8 x + 12} + \frac{672 x}{x^{2} + 8 x + 12} + \frac{864}{x^{2} + 8 x + 12}}\]
Factored
\[\frac{\frac{x}{8 x + 48}}{\frac{{x}^{2} + 11 x + 18}{{x}^{2} + 8 x + 12}} = \frac{x}{8 \left(x + 9\right)}\]