(1/k-k/2)K(k) - kE(k)

asked by guest
on Oct 26, 2024 at 1:13 pm



You asked:

Evaluate the expression: \(\left(\frac{1}{k} - \frac{k}{2}\right) \cdot K\left( k \right) - k \cdot E\left( k \right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left(\frac{1}{k} - \frac{k}{2}\right) \cdot K\left( k \right) - k \cdot E\left( k \right) = - k E{\left(k \right)} + \left(- \frac{k}{2} + \frac{1}{k}\right) K{\left(k \right)} \)

Expanded

\[\left(\frac{1}{k} - \frac{k}{2}\right) \cdot K\left( k \right) - k \cdot E\left( k \right) = - k E{\left(k \right)} - \frac{k K{\left(k \right)}}{2} + \frac{K{\left(k \right)}}{k}\]

Factored

\[\left(\frac{1}{k} - \frac{k}{2}\right) \cdot K\left( k \right) - k \cdot E\left( k \right) = - \frac{2 k^{2} E{\left(k \right)} + k^{2} K{\left(k \right)} - 2 K{\left(k \right)}}{2 k}\]

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