((2000 – 5)/((2000+2005)/2)) / ((90-100)/((90+100)/2))

asked by guest
on Nov 17, 2024 at 12:44 am



You asked:

Evaluate the expression: \(\frac{\frac{2000 - 5}{\frac{2000 + 2005}{2}}}{\frac{90 - 100}{\frac{90 + 100}{2}}}\)

MathBot Answer:

\[\frac{\frac{2000 - 5}{\frac{2000 + 2005}{2}}}{\frac{90 - 100}{\frac{90 + 100}{2}}} = - \frac{2527}{267} = -9.\overline{46441947565543071161048689138576779026217228}\]

\[\begin{aligned}\frac{\frac{2000 - 5}{\frac{2000 + 2005}{2}}}{\frac{90 - 100}{\frac{90 + 100}{2}}}& = \left(2000 - 5\right) \cdot \frac{1}{\left(2000 + 2005\right) \cdot \frac{1}{2}} \cdot \frac{1}{\left(90 - 100\right) \cdot \frac{1}{\left(90 + 100\right) \cdot \frac{1}{2}}}\\& = 1995 \cdot \frac{1}{\left(2000 + 2005\right) \cdot \frac{1}{2}} \cdot \frac{1}{\left(90 - 100\right) \cdot \frac{1}{\left(90 + 100\right) \cdot \frac{1}{2}}}\\& = 1995 \cdot \frac{1}{\frac{4005}{2}} \cdot \frac{1}{\left(90 - 100\right) \cdot \frac{1}{\left(90 + 100\right) \cdot \frac{1}{2}}}\\& = 1995 \cdot \frac{2}{4005} \cdot \frac{1}{\left(90 - 100\right) \cdot \frac{1}{\left(90 + 100\right) \cdot \frac{1}{2}}}\\& = 1995 \cdot \frac{2}{4005} \cdot \frac{1}{-10 \cdot \frac{1}{\left(90 + 100\right) \cdot \frac{1}{2}}}\\& = 1995 \cdot \frac{2}{4005} \cdot \frac{1}{-10 \cdot \frac{1}{\frac{190}{2}}}\\& = 1995 \cdot \frac{2}{4005} \cdot \frac{1}{\frac{-10}{95}}\\& = 1995 \cdot \frac{2}{4005} \cdot \frac{1}{- \frac{2}{19}}\\& = 1995 \cdot - \frac{19}{4005}\\& = - \frac{2527}{267}\end{aligned}\]

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