$\frac{x^2 + 8x + 16\}{x^2 - 16\}$ รท $\frac{x^2 - 3x - 28\}{x - 7\}$

asked by guest
on Sep 22, 2024 at 4:31 pm



You asked:

Evaluate the expression: \(\frac{\frac{{x}^{2} + 8 x + 16}{{x}^{2} - 16}}{\frac{{x}^{2} - 3 x - 28}{x - 7}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{{x}^{2} + 8 x + 16}{{x}^{2} - 16}}{\frac{{x}^{2} - 3 x - 28}{x - 7}} = \frac{\left(x - 7\right) \left(x^{2} + 8 x + 16\right)}{\left(x^{2} - 16\right) \left(x^{2} - 3 x - 28\right)} \)

Expanded

\[\frac{\frac{{x}^{2} + 8 x + 16}{{x}^{2} - 16}}{\frac{{x}^{2} - 3 x - 28}{x - 7}} = \frac{x^{2}}{\frac{x^{4}}{x - 7} - \frac{3 x^{3}}{x - 7} - \frac{44 x^{2}}{x - 7} + \frac{48 x}{x - 7} + \frac{448}{x - 7}} + \frac{8 x}{\frac{x^{4}}{x - 7} - \frac{3 x^{3}}{x - 7} - \frac{44 x^{2}}{x - 7} + \frac{48 x}{x - 7} + \frac{448}{x - 7}} + \frac{16}{\frac{x^{4}}{x - 7} - \frac{3 x^{3}}{x - 7} - \frac{44 x^{2}}{x - 7} + \frac{48 x}{x - 7} + \frac{448}{x - 7}}\]

Factored

\[\frac{\frac{{x}^{2} + 8 x + 16}{{x}^{2} - 16}}{\frac{{x}^{2} - 3 x - 28}{x - 7}} = \frac{1}{x - 4}\]

+ Submit Question