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.