Certainly! Let's simplify the given expression step-by-step.
We are given the expression:
[tex]\[
\frac{2x + 4}{2x - 16}
\][/tex]
### Step 1: Factor the numerator and the denominator
First, let's factor out common terms in both the numerator and the denominator.
In the numerator [tex]\(2x + 4\)[/tex], we can factor out a 2:
[tex]\[
2x + 4 = 2(x + 2)
\][/tex]
In the denominator [tex]\(2x - 16\)[/tex], we can factor out a 2:
[tex]\[
2x - 16 = 2(x - 8)
\][/tex]
### Step 2: Substitute the factored forms back into the expression
Now we substitute these factored forms back into the original expression:
[tex]\[
\frac{2(x + 2)}{2(x - 8)}
\][/tex]
### Step 3: Cancel common factors
Since there is a common factor of 2 in both the numerator and the denominator, we can cancel it out:
[tex]\[
\frac{2(x + 2)}{2(x - 8)} = \frac{x + 2}{x - 8}
\][/tex]
### Conclusion
Thus, the simplified form of the given expression [tex]\(\frac{2x + 4}{2x - 16}\)[/tex] is:
[tex]\[
\frac{x + 2}{x - 8}
\][/tex]
