Sure, let's simplify the expression step-by-step.
Given:
[tex]\[
\frac{2 y}{y+2} + \frac{4}{y+2}
\][/tex]
1. Notice that both terms in the sum have the same denominator, [tex]\( y + 2 \)[/tex]. When adding fractions with the same denominator, you simply add the numerators together:
[tex]\[
\frac{2 y + 4}{y+2}
\][/tex]
2. Next, factor the numerator:
[tex]\[
2 y + 4 = 2(y + 2)
\][/tex]
So the expression now becomes:
[tex]\[
\frac{2(y + 2)}{y + 2}
\][/tex]
3. Since the numerator and the denominator are the same (except for the factor 2 in the numerator), we can cancel out [tex]\( y + 2 \)[/tex]:
[tex]\[
\frac{2(y + 2)}{y + 2} = 2
\][/tex]
Thus, the expression simplifies to [tex]\( 2 \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
