Certainly! Let's go through the process of subtracting the given rational expressions step by step.
### Problem Statement
We need to subtract two rational expressions with numerators [tex]\( x + 1 \)[/tex] and [tex]\( x - 2 \)[/tex].
### Step-by-Step Solution
1. Write Down the Numerators:
- The first numerator is [tex]\( x + 1 \)[/tex].
- The second numerator is [tex]\( x - 2 \)[/tex].
2. Set Up the Subtraction:
To subtract the second numerator from the first, we will write:
[tex]\[
(x + 1) - (x - 2)
\][/tex]
3. Distribute the Negative Sign:
We need to ensure that all terms in the second numerator are subtracted. Distribute the negative sign to each term inside the parentheses:
[tex]\[
(x + 1) - (x - 2) = x + 1 - x + 2
\][/tex]
4. Combine Like Terms:
Combine the like terms to simplify the expression:
- The [tex]\( x \)[/tex] terms: [tex]\( x - x = 0 \)[/tex].
- The constants: [tex]\( 1 + 2 = 3 \)[/tex].
5. Result:
After combining the like terms, the simplified form of the difference of the numerators is:
[tex]\[
3
\][/tex]
Thus, the simplified numerator of the difference between the given rational expressions is [tex]\( 3 \)[/tex].
