Finding Least Common Denominator of Fractions
The image shows three fractions:
\[ \frac{x}{x - 2}, \quad \frac{3x}{x - 2}, \quad \frac{4}{x + 1}. \]
The question asks to find the least common denominator (LCD) of these fractions.
The denominators are \( x - 2 \), \( x - 2 \), and \( x + 1 \). To find the LCD, we look for a common denominator that each of these can divide into without leaving a remainder.
Since \( x - 2 \) and \( x + 1 \) are different linear factors and neither divides the other, the LCD is simply the product of the unique factors \( x - 2 \) and \( x + 1 \). Therefore, the LCD is:
\[ (x - 2)(x + 1) = x^2 + x - 2x - 2 = x^2 - x - 2. \]
This is the LCD for the given fractions.
