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The image you provided seems to show a mathematical expression related to Laplace transforms, possibly focusing on inverse Laplace transforms. The equation appears to be:

\[
\frac{V_o(s)}{V_i(s)} = \frac{s^2 - 2s + 7}{s^3 + 5}
\]

This likely represents a transfer function \( H(s) = \frac{V_o(s)}{V_i(s)} \), which you might want to transform back into the time domain using the inverse Laplace transform.

### To find the inverse Laplace transform of:

\[
H(s) = \frac{s^2 - 2s + 7}{s^3 + 5}
\]

The process generally involves:
1. Factoring or simplifying the denominator to check for poles and partial fractions.
2. Applying known Laplace transform pairs or using partial fraction decomposition to break it into simpler terms.
3. Taking the inverse Laplace of each term individually.

Would you like me to proceed with finding the inverse Laplace transform step by step, or do you need help with a specific part of this process?

### Here are 5 related questions:
1. Do you need help with factoring the denominator \(s^3 + 5\)?
2. Would you like a breakdown of how to perform partial fraction decomposition?
3. Are you familiar with the inverse Laplace transform table, or should I provide some common pairs?
4. Do you need clarification on the significance of poles in the Laplace domain?
5. Are you looking for a numerical solution or a general expression for the inverse Laplace?

#### Tip:
When working with Laplace transforms, it's useful to have a table of standard transforms and their inverses on hand for quick reference.

Learn how to find the inverse Laplace transform of the transfer function H(s) = (s^2 - 2s + 7) / (s^3 + 5). This problem explores key concepts of the Laplace transform, inverse Laplace, and transfer functions. Suitable for advanced undergraduate or graduate students.

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