Question

Find the least common denominator for the following rational expressions.
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(r – 1)(r – 4)(r – 5)

(r – 1)(r + 4)(r – 5)

(r – 1)(r + 1)(r – 4)(r – 5)

(r – 1)(r + 1)(r + 4)(r – 5)

Answer 1

LCD = (r − 1)(r − 5)(r − 4)(r + 4)(r + 1)

Reason: the LCD must include each distinct linear factor appearing in any denominator (each to the first power), so include (r−1), (r−5), (r−4), (r+4), and (r+1).