(x+2)/(x^(2)-4)*(x^(3)-8)/(x-4)

asked by guest
on Nov 27, 2024 at 12:03 pm



You asked:

Evaluate the expression: \(\frac{\frac{x + 2}{{x}^{2} - 4} \cdot \left({x}^{3} - 8\right)}{x - 4}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{x + 2}{{x}^{2} - 4} \cdot \left({x}^{3} - 8\right)}{x - 4} = \frac{\left(x^{3} - 8\right) \left(x + 2\right)}{\left(x^{2} - 4\right) \left(x - 4\right)} \)

Expanded

\[\frac{\frac{x + 2}{{x}^{2} - 4} \cdot \left({x}^{3} - 8\right)}{x - 4} = \frac{x^{4}}{x^{3} - 4 x^{2} - 4 x + 16} + \frac{2 x^{3}}{x^{3} - 4 x^{2} - 4 x + 16} - \frac{8 x}{x^{3} - 4 x^{2} - 4 x + 16} - \frac{16}{x^{3} - 4 x^{2} - 4 x + 16}\]

Factored

\[\frac{\frac{x + 2}{{x}^{2} - 4} \cdot \left({x}^{3} - 8\right)}{x - 4} = \frac{x^{2} + 2 x + 4}{x - 4}\]

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