$\frac{8(10-x)}{(x+1)(x-10)}$ $\frac{x-8}{(x-8)(x+1)}$

asked by guest
on Sep 21, 2024 at 4:36 am



You asked:

Evaluate the expression: \(\frac{8 \cdot \left(10 - x\right)}{\left(x + 1\right) \cdot \left(x - 10\right)} \cdot \frac{x - 8}{\left(x - 8\right) \cdot \left(x + 1\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{8 \cdot \left(10 - x\right)}{\left(x + 1\right) \cdot \left(x - 10\right)} \cdot \frac{x - 8}{\left(x - 8\right) \cdot \left(x + 1\right)} = \frac{8 \cdot \left(10 - x\right)}{\left(x - 10\right) \left(x + 1\right)^{2}} \)

Expanded

\[\frac{8 \cdot \left(10 - x\right)}{\left(x + 1\right) \cdot \left(x - 10\right)} \cdot \frac{x - 8}{\left(x - 8\right) \cdot \left(x + 1\right)} = - \frac{8 x^{2}}{x^{4} - 16 x^{3} + 45 x^{2} + 142 x + 80} + \frac{144 x}{x^{4} - 16 x^{3} + 45 x^{2} + 142 x + 80} - \frac{640}{x^{4} - 16 x^{3} + 45 x^{2} + 142 x + 80}\]

Factored

\[\frac{8 \cdot \left(10 - x\right)}{\left(x + 1\right) \cdot \left(x - 10\right)} \cdot \frac{x - 8}{\left(x - 8\right) \cdot \left(x + 1\right)} = - \frac{8}{\left(x + 1\right)^{2}}\]

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