Of course! Let's simplify the given expression step-by-step:
We start with the expression:
[tex]\[
\frac{2x + 4}{2x - 16}
\][/tex]
### Step 1: Factor the Numerator and Denominator
First, let's look at the numerator [tex]\(2x + 4\)[/tex] and the denominator [tex]\(2x - 16\)[/tex]. We can factor both expressions by identifying the greatest common factor (GCF).
For the numerator [tex]\(2x + 4\)[/tex], the GCF is 2:
[tex]\[
2x + 4 = 2(x + 2)
\][/tex]
For the denominator [tex]\(2x - 16\)[/tex], the GCF is also 2:
[tex]\[
2x - 16 = 2(x - 8)
\][/tex]
### Step 2: Rewrite the Fraction
Now, we can rewrite the original fraction by substituting the factored forms:
[tex]\[
\frac{2(x + 2)}{2(x - 8)}
\][/tex]
### Step 3: Cancel the Common Factors
The 2 in the numerator and the 2 in the denominator are common factors and can be canceled out:
[tex]\[
\frac{2(x + 2)}{2(x - 8)} = \frac{x + 2}{x - 8}
\][/tex]
### Step 4: Simplified Expression
After canceling the common factor, we are left with:
[tex]\[
\frac{x + 2}{x - 8}
\][/tex]
So, the simplified form of the given expression [tex]\(\frac{2x + 4}{2x - 16}\)[/tex] is:
[tex]\[
\boxed{\frac{x + 2}{x - 8}}
\][/tex]
