The expression in the image is:

$\frac{x - 1}{x + 1} + \frac{1}{x}.$

Let’s simplify this step by step.

Step 1: Find a common denominator

The denominators are $x + 1$ and $x$. The least common denominator (LCD) is:

$x(x + 1).$

Step 2: Rewrite each fraction with the LCD

Rewriting each term:

1. $\frac{x - 1}{x + 1}$ becomes $\frac{x(x - 1)}{x(x + 1)}$,
2. $\frac{1}{x}$ becomes $\frac{x + 1}{x(x + 1)}$.

So the expression becomes:

$\frac{x(x - 1)}{x(x + 1)} + \frac{x + 1}{x(x + 1)}.$

Step 3: Combine the fractions

Now that the denominators are the same, combine the numerators:

$\frac{x(x - 1) + (x + 1)}{x(x + 1)}.$

Step 4: Simplify the numerator

Expand $x(x - 1)$:

$x(x - 1) = x^2 - x.$

Now add $(x^2 - x)$ and $(x + 1)$:

$x^2 - x + x + 1 = x^2 + 1.$

So the numerator is $x^2 + 1$.

Step 5: Write the final simplified expression

The simplified expression is:

$\frac{x^2 + 1}{x(x + 1)}.$

Let me know if you want further clarification!

Here are 5 related questions to explore further:

1. What would happen if $x = -1$?
2. How do you determine the domain of this expression?
3. What is the simplified form of $\frac{x^2 - 1}{x^2 + x}$?
4. How would you approach this if asked to compute a numerical value (e.g., $x = 2$)?
5. Can this fraction be factored further?

Tip: Always check for restrictions on the variable when simplifying fractions involving denominators!