Question
Hind the least common denominator of \( \frac{x}{x-5} \) and \( \frac{4 x}{x-3} \), \( \square \)
Ask by Griffin Phillips. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The least common denominator is (x−5)(x−3).
Solution
To find the least common denominator (LCD) of the fractions x/(x−5) and 4x/(x−3), start by looking at the denominators. The first denominator is (x−5) and the second is (x−3). Since these two expressions have no common factors, the LCD is simply the product of the two:
LCD = (x−5)(x−3).
Thus, the least common denominator is (x−5)(x−3).
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Simplify this solution Extra Insights
To find the least common denominator (LCD) of the fractions \( \frac{x}{x-5} \) and \( \frac{4x}{x-3} \), we need to look at the denominators of both fractions, which are \( x - 5 \) and \( x - 3 \). The LCD is simply the product of these two distinct linear factors, which would be \( (x - 5)(x - 3) \). Thus, the least common denominator is \( (x - 5)(x - 3) \). However, always double-check any algebraic expressions for factoring or simplification opportunities before assuming you've got the final answer. In cases where there's a common factor among more than two fractions, ensure you're not missing a simpler LCD that incorporates any shared factors.
