https://file.aiquickdraw.com/mathbot/file/17279722529803lg0qw8c.jpg

The given mathematical expression in the image is:

\[
\frac{\mu_0 N I r^2}{2\left(r^2 + h^2\right)^{3/2}} - \frac{\mu_0 N I}{2h}
\]

Let's simplify this step by step.

### Step 1: Factor out common terms
Notice that both terms in the expression have the common factors \(\frac{\mu_0 N I}{2}\). So, we can factor those terms out:

\[
\frac{\mu_0 N I}{2} \left( \frac{r^2}{(r^2 + h^2)^{3/2}} - \frac{1}{h} \right)
\]

### Step 2: Combine the terms inside the parentheses
Now we need to combine the terms \(\frac{r^2}{(r^2 + h^2)^{3/2}}\) and \(\frac{1}{h}\). Since they don't have the same denominator, we'll leave them as they are unless further combination is needed.

Thus, the simplified expression is:

\[
\frac{\mu_0 N I}{2} \left( \frac{r^2}{(r^2 + h^2)^{3/2}} - \frac{1}{h} \right)
\]

This is the most simplified form of the given expression without specific numerical values or further assumptions about \(r\) and \(h\).

Would you like further details on this simplification, or do you have any specific questions?

### Related Questions:
1. What physical problem does this expression represent?
2. How does the parameter \(r^2 + h^2\) affect the simplification?
3. Can you evaluate this expression for specific values of \(r\) and \(h\)?
4. How does this expression relate to magnetic fields?
5. What are the units of \(\mu_0\) in the context of this equation?

#### Tip:
When simplifying complex fractions, always look for common factors that can be factored out to reduce the expression easily.

Simplify the expression \(\frac{\mu_0 N I r^2}{2(r^2 + h^2)^{3/2}} - \frac{\mu_0 N I}{2h}\).

Learn how to simplify the magnetic field expression \(\frac{\mu_0 N I r^2}{2(r^2 + h^2)^{3/2}} - \frac{\mu_0 N I}{2h}\). This problem covers key concepts in electromagnetism and algebra, suitable for advanced high school or college-level students.

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