Answer :
To simplify the given expression [tex]\(\frac{2x + 2}{x + 1}\)[/tex], follow these steps:
1. Factor the Numerator (if possible):
The numerator [tex]\(2x + 2\)[/tex] can be factored:
[tex]\[ 2x + 2 = 2(x + 1) \][/tex]
2. Rewrite the Expression:
Substitute the factored form of the numerator into the expression:
[tex]\[ \frac{2(x + 1)}{x + 1} \][/tex]
3. Simplify by Cancelling Common Factors:
Notice that both the numerator and the denominator have a common factor of [tex]\(x + 1\)[/tex]. As long as [tex]\(x \neq -1\)[/tex] (to avoid division by zero), we can cancel [tex]\(x + 1\)[/tex] from both the numerator and the denominator:
[tex]\[ \frac{2(x + 1)}{x + 1} = 2 \][/tex]
4. Conclusion:
The simplified form of the expression [tex]\(\frac{2x + 2}{x + 1}\)[/tex] is [tex]\(2\)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
Therefore, the simplified expression is [tex]\(2\)[/tex]. As per the given options, the correct choice is:
[tex]\[ \text{C) 2} \][/tex]
1. Factor the Numerator (if possible):
The numerator [tex]\(2x + 2\)[/tex] can be factored:
[tex]\[ 2x + 2 = 2(x + 1) \][/tex]
2. Rewrite the Expression:
Substitute the factored form of the numerator into the expression:
[tex]\[ \frac{2(x + 1)}{x + 1} \][/tex]
3. Simplify by Cancelling Common Factors:
Notice that both the numerator and the denominator have a common factor of [tex]\(x + 1\)[/tex]. As long as [tex]\(x \neq -1\)[/tex] (to avoid division by zero), we can cancel [tex]\(x + 1\)[/tex] from both the numerator and the denominator:
[tex]\[ \frac{2(x + 1)}{x + 1} = 2 \][/tex]
4. Conclusion:
The simplified form of the expression [tex]\(\frac{2x + 2}{x + 1}\)[/tex] is [tex]\(2\)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
Therefore, the simplified expression is [tex]\(2\)[/tex]. As per the given options, the correct choice is:
[tex]\[ \text{C) 2} \][/tex]
