Get comprehensive solutions to your problems with IDNLearn.com. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
Sagot :
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].
### 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].
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.