p / ( x - p*k ) + (1- p) / ( y - (1 - p)*k)

asked by guest
on Jan 11, 2025 at 4:51 pm



You asked:

Evaluate the expression: \(\frac{p}{x - p k} + \frac{1 - p}{y - \left(1 - p\right) \cdot k}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{p}{x - p k} + \frac{1 - p}{y - \left(1 - p\right) \cdot k} = \frac{p}{- k p + x} + \frac{1 - p}{- k \left(1 - p\right) + y} \)

Expanded

\[\frac{p}{x - p k} + \frac{1 - p}{y - \left(1 - p\right) \cdot k} = - \frac{p}{k p - k + y} + \frac{p}{- k p + x} + \frac{1}{k p - k + y}\]

Factored

\[\frac{p}{x - p k} + \frac{1 - p}{y - \left(1 - p\right) \cdot k} = - \frac{2 p^{2} k - 2 k p - p x + p y + x}{\left(k p - x\right) \left(k p - k + y\right)}\]

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