8(10-x) over (x+1)(x-10) divided by x-8 over (x-8)(x+1)

asked by guest
on Sep 21, 2024 at 4:33 am



You asked:

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

MathBot Answer:

Evaluated



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

Expanded

\[\frac{\frac{8 \cdot \left(10 - x\right)}{\left(x + 1\right) \cdot \left(x - 10\right)}}{x} - \frac{8}{\left(x - 8\right) \cdot \left(x + 1\right)} = - \frac{8 x}{x^{3} - 9 x^{2} - 10 x} + \frac{80}{x^{3} - 9 x^{2} - 10 x} - \frac{8}{x^{2} - 7 x - 8}\]

Factored

\[\frac{\frac{8 \cdot \left(10 - x\right)}{\left(x + 1\right) \cdot \left(x - 10\right)}}{x} - \frac{8}{\left(x - 8\right) \cdot \left(x + 1\right)} = - \frac{16 \left(x - 4\right)}{x \left(x - 8\right) \left(x + 1\right)}\]

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