The expression you provided is:

\[
\left(x - 1\right) + \left(x + 1\right)
\]

Now, let's simplify it step by step:

1. Combine the like terms:
   \[
   (x - 1) + (x + 1) = x + x - 1 + 1
   \]

2. Simplify further by canceling out $-1$ and $+1$:
   \[
   x + x = 2x
   \]

Thus, the simplified expression is:

\[
2x
\]

Would you like any additional details on the steps? 

Here are 5 related questions to explore further:
1. What happens if we add constants to this expression, like $ \left(2x - 1\right) + \left(3x + 1\right) $?
2. How do we simplify more complex algebraic expressions with different variables?
3. Can this expression be used in a system of equations? How would we solve that?
4. What if we include exponents, such as $ \left(x^2 - 1\right) + \left(x^2 + 1\right) $?
5. How does this simplify if $x$ is given a specific value?

**Tip:** Always combine like terms (such as variables or constants) first to simplify expressions quickly.

$$ \left(x-1\right) + \left(x+1\right) $$

Explore how to simplify the algebraic expression (x-1) + (x+1) step by step. Learn key concepts of combining like terms and the basic properties of addition. This guide is suitable for students in Grades 6-8.

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