Question - Finding Least Common Denominator of Fractions
Solution:
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.
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