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Advanced Algebra B
Working with Rationals Assessment

Simplify each expression. SHOW YOUR WORK!

1) [tex]\frac{2x+2}{x+1}[/tex]

A) [tex]-\frac{1}{2}[/tex]
B) [tex]\frac{7}{5x+7}[/tex]
C) 2
D) [tex]\frac{1}{x+1}[/tex]

Sagot :

GinnyAnswer
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]
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