Sure, let's go through the process step by step.
### Simplifying the First Expression:
The given expression is:
[tex]\[ \frac{3x + 3}{3} + 3 \][/tex]
Step 1: Simplify the fraction:
[tex]\[ \frac{3x + 3}{3} = \frac{3x}{3} + \frac{3}{3} = x + 1 \][/tex]
Step 2: Add 3 to the simplified expression:
[tex]\[ x + 1 + 3 = x + 4 \][/tex]
So, the simplified form of the first expression is [tex]\( x + 4 \)[/tex].
### Simplifying the Second Expression:
The given expression is:
[tex]\[ \frac{3x}{4} - \frac{x - y}{3} \][/tex]
Step 1: Find a common denominator for the two fractions. The common denominator for 4 and 3 is 12.
Step 2: Rewrite each fraction with the common denominator:
[tex]\[ \frac{3x}{4} = \frac{3x \cdot 3}{4 \cdot 3} = \frac{9x}{12} \][/tex]
[tex]\[ \frac{x - y}{3} = \frac{(x - y) \cdot 4}{3 \cdot 4} = \frac{4(x - y)}{12} \][/tex]
Step 3: Combine the fractions:
[tex]\[ \frac{9x}{12} - \frac{4(x - y)}{12} = \frac{9x - 4(x - y)}{12} \][/tex]
Step 4: Distribute [tex]\( -4 \)[/tex] in the numerator:
[tex]\[ 9x - 4(x - y) = 9x - 4x + 4y = 5x + 4y \][/tex]
Step 5: Put it back over the common denominator:
[tex]\[ \frac{5x + 4y}{12} \][/tex]
At this point, the simplified form of the second expression is:
[tex]\[ \frac{5x}{12} + \frac{y}{3} \][/tex]
So the fully simplified form of the second expression is:
[tex]\[ \frac{5x}{12} + \frac{y}{3} \][/tex]
### Summary
1. The simplified form of [tex]\(\frac{3x + 3}{3} + 3\)[/tex] is [tex]\( x + 4 \)[/tex].
2. The simplified form of [tex]\(\frac{3x}{4} - \frac{x - y}{3}\)[/tex] is [tex]\( \frac{5x}{12} + \frac{y}{3} \)[/tex].
