Question
1. Simplify fully \[ \frac{x}{3}+\frac{x}{4} \]
Ask by Page Paul. in South Africa
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(\frac{7x}{12}\).
Solution
To add the fractions, first find a common denominator. The least common multiple of 3 and 4 is 12.
Rewrite each fraction with the denominator 12:
• x/3 = (4x)/12,
• x/4 = (3x)/12.
Now, add the two fractions:
(4x)/12 + (3x)/12 = (4x + 3x)/12 = (7x)/12.
Thus, the simplified expression is (7x)/12.
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Simplify this solution Beyond the Answer
To simplify \(\frac{x}{3}+\frac{x}{4}\), we need a common denominator. The least common multiple of 3 and 4 is 12. Rewriting the fractions, we get: \[ \frac{x}{3} = \frac{4x}{12} \quad \text{and} \quad \frac{x}{4} = \frac{3x}{12} \] Now we can combine them: \[ \frac{4x}{12} + \frac{3x}{12} = \frac{4x + 3x}{12} = \frac{7x}{12} \] So the fully simplified expression is \(\frac{7x}{12}\).
