Sure, let's solve the given expression step by step for [tex]\( y = 2 \)[/tex].
We need to evaluate the expression:
[tex]\[ \frac{2-y}{4+y} + \frac{3(y+2)}{y} \][/tex]
1. Substitute [tex]\( y = 2 \)[/tex] into the first fraction:
[tex]\[ \frac{2-y}{4+y} = \frac{2-2}{4+2} \][/tex]
2. Simplify the first fraction:
[tex]\[ \frac{2-2}{4+2} = \frac{0}{6} = 0 \][/tex]
So, the first fraction is [tex]\( 0 \)[/tex].
3. Substitute [tex]\( y = 2 \)[/tex] into the second fraction:
[tex]\[ \frac{3(y+2)}{y} = \frac{3(2+2)}{2} \][/tex]
4. Simplify the second fraction:
[tex]\[ \frac{3(2+2)}{2} = \frac{3 \cdot 4}{2} = \frac{12}{2} = 6 \][/tex]
So, the second fraction is [tex]\( 6 \)[/tex].
5. Sum the value of the two fractions:
[tex]\[ 0 + 6 = 6 \][/tex]
Therefore, the value of the expression when [tex]\( y = 2 \)[/tex] is 6.
So, the correct answer is:
[tex]\[ \boxed{6} \][/tex]
