\frac{\left(-1\right)^3-3\left(-1\right)^2-2\left(-1\right)-5}{2\left(-1\right)^2-9\left(-1\right)+2}

asked by guest
on Sep 16, 2024 at 12:56 pm



You asked:

Evaluate the expression: \(\frac{{\left( -1 \right)}^{3} - 3 \cdot {\left( -1 \right)}^{2} - 2 \cdot -1 - 5}{2 \cdot {\left( -1 \right)}^{2} - 9 \cdot -1 + 2}\)

MathBot Answer:

\[\frac{{\left( -1 \right)}^{3} - 3 \cdot {\left( -1 \right)}^{2} - 2 \cdot -1 - 5}{2 \cdot {\left( -1 \right)}^{2} - 9 \cdot -1 + 2} = - \frac{7}{13} = -0.\overline{538461}\]

\[\begin{aligned}\frac{{\left( -1 \right)}^{3} - 3 \cdot {\left( -1 \right)}^{2} - 2 \cdot -1 - 5}{2 \cdot {\left( -1 \right)}^{2} - 9 \cdot -1 + 2}& = \left(\left(-1\right)^{3} - 3 \cdot \left(-1\right)^{2} - 2 \cdot -1 - 5\right) \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = \left(-1 - 3 \cdot \left(-1\right)^{2} - 2 \cdot -1 - 5\right) \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = \left(-1 - 3 \cdot 1 - 2 \cdot -1 - 5\right) \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = \left(-1 - 3 - 2 \cdot -1 - 5\right) \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = \left(-1 - 3 - -2 - 5\right) \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = \left(-1 - 3 + 2 - 5\right) \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = \left(-4 + 2 - 5\right) \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = \left(-2 - 5\right) \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = -7 \cdot \frac{1}{2 \cdot \left(-1\right)^{2} - 9 \cdot -1 + 2}\\& = -7 \cdot \frac{1}{2 \cdot 1 - 9 \cdot -1 + 2}\\& = -7 \cdot \frac{1}{2 - 9 \cdot -1 + 2}\\& = -7 \cdot \frac{1}{2 - -9 + 2}\\& = -7 \cdot \frac{1}{2 + 9 + 2}\\& = -7 \cdot \frac{1}{11 + 2}\\& = \frac{-7}{13}\\& = - \frac{7}{13}\end{aligned}\]

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