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Rational Expressions

Which of the following did you include in your description?

A. You must subtract all terms of the numerator being subtracted out, not just the first term.
B. The negative 2 should have been subtracted out to get a numerator of [tex]$x+1-x+2$[/tex].
C. The simplified numerator of the difference should be 3, not -1.

Sagot :

GinnyAnsweridn
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].
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