Sure, let's simplify the given expression step by step:
The given expression is:
[tex]\[
\frac{4x + 4b}{2x + 2b}
\][/tex]
Step 1: Identify and factor out the common factors in the numerator and the denominator.
In the numerator [tex]\(4x + 4b\)[/tex]:
Both terms have a common factor of 4, so we can factor out 4:
[tex]\[
4x + 4b = 4(x + b)
\][/tex]
In the denominator [tex]\(2x + 2b\)[/tex]:
Both terms have a common factor of 2, so we can factor out 2:
[tex]\[
2x + 2b = 2(x + b)
\][/tex]
Step 2: Substitute the factored expressions back into the fraction:
[tex]\[
\frac{4(x + b)}{2(x + b)}
\][/tex]
Step 3: Simplify the fraction by canceling out the common factor [tex]\((x + b)\)[/tex] from the numerator and the denominator:
[tex]\[
\frac{4(x + b)}{2(x + b)} = \frac{4}{2}
\][/tex]
Step 4: Simplify the resulting fraction:
[tex]\[
\frac{4}{2} = 2
\][/tex]
So, the simplified form of the given expression [tex]\(\frac{4x + 4b}{2x + 2b}\)[/tex] is:
[tex]\[
2
\][/tex]
