The mathematical expression shown in the image is:

$\frac{x^2 + x}{x + 1}$

To simplify this expression:

Step 1: Factorize the numerator

The numerator $x^2 + x$ can be factorized by taking $x$ as the common factor: $x^2 + x = x(x + 1)$

Step 2: Write the expression in its factored form

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

Step 3: Simplify the expression

If $x + 1 \neq 0$ (i.e., $x \neq -1$), the $x + 1$ terms cancel out: $\frac{x(x + 1)}{x + 1} = x$

Final Answer:

The simplified expression is: $x \quad \text{for } x \neq -1$

Would you like further clarification or have additional questions?

Here are 5 related questions you might find helpful:

1. How does factorization work for higher-degree polynomials?
2. What happens if $x + 1 = 0$? Why can’t we divide by zero?
3. Can this simplification be visualized graphically?
4. How would you handle this expression if it were part of an equation to solve?
5. What are some common mistakes to avoid when simplifying rational expressions?

Tip: Always check for restrictions on the variable (like $x \neq -1$ here) when simplifying rational expressions!