Question
Find the least common denominator of \( \frac{3}{x+10} \) and \( \frac{2}{x-10} \) \( \square \)
Ask by Marsh Medina. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The least common denominator is (x + 10)(x - 10) or x² - 100.
Solution
To find the least common denominator (LCD) for the fractions 3/(x + 10) and 2/(x - 10), we first identify the denominators:
• The first denominator is (x + 10).
• The second denominator is (x - 10).
Since these are two distinct binomials with no common factors, the LCD is simply their product:
LCD = (x + 10)(x - 10).
This expression can also be simplified as a difference of squares:
(x + 10)(x - 10) = x² - 100.
Therefore, the least common denominator is (x + 10)(x - 10) or equivalently x² - 100.
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Simplify this solution Mind Expander
To find the least common denominator (LCD) of the fractions \( \frac{3}{x+10} \) and \( \frac{2}{x-10} \), we need to identify the denominators first. In this case, they are \( x + 10 \) and \( x - 10 \). The LCD is simply the product of these two distinct denominators since they have no common factors. Thus, the least common denominator is: \[ (x + 10)(x - 10) = x^2 - 100 \] Now you can rewrite both fractions with the common denominator of \( x^2 - 100 \) for easier addition or subtraction!
