The expression shown in the image is:

$\frac{p+q}{p-q} + \frac{p-q}{p+q}$

Let's solve this step by step.

Step 1: Find the common denominator

The common denominator between $\frac{p+q}{p-q}$ and $\frac{p-q}{p+q}$ is $(p+q)(p-q)$.

Step 2: Rewrite the expression with the common denominator

$\frac{(p+q)^2 + (p-q)^2}{(p-q)(p+q)}$

Step 3: Expand the numerator

$(p+q)^2 = p^2 + 2pq + q^2$ $(p-q)^2 = p^2 - 2pq + q^2$

So, the expression becomes: $\frac{p^2 + 2pq + q^2 + p^2 - 2pq + q^2}{(p-q)(p+q)}$

Step 4: Simplify the numerator

$p^2 + 2pq + q^2 + p^2 - 2pq + q^2 = 2p^2 + 2q^2$

Thus, the expression is now: $\frac{2p^2 + 2q^2}{(p-q)(p+q)}$

Step 5: Factor out the 2 in the numerator

$\frac{2(p^2 + q^2)}{(p-q)(p+q)}$

Final Answer:

The simplified result is: $\boxed{\frac{2(p^2 + q^2)}{(p-q)(p+q)}}$

Would you like more details on any part of this solution?

Here are 5 related questions you might find helpful:

1. How do you simplify expressions with common denominators?
2. What is the process for expanding binomials like $(p+q)^2$?
3. Can you derive the difference of squares formula from $(p+q)(p-q)$?
4. How can we generalize this process for similar expressions?
5. What happens if $p = q$ in this expression?

Tip: When adding fractions, always look for a common denominator before attempting to simplify!