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Find the LCD of the rational expressions in the list. (7)/(5x+15),(2)/(9x-36) The LCD (least common denominator) is ◻ (Type your answer in factored form.)

Find the LCD of the rational expressions in the list.\newline75x+15,29x−36 \frac{7}{5 x+15}, \frac{2}{9 x-36} \newlineThe LCD (least common denominator) is □ \square (Type your answer in factored form.)

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Full solution

Q. Find the LCD of the rational expressions in the list.\newline75x+15,29x−36 \frac{7}{5 x+15}, \frac{2}{9 x-36} \newlineThe LCD (least common denominator) is □ \square (Type your answer in factored form.)
  1. Factor Denominators: Factor the denominators of both rational expressions.\newlineFor the first expression, (5x+15)(5x+15), we can factor out a 55 to get 5(x+3)5(x+3).\newlineFor the second expression, (9x−36)(9x-36), we can factor out a 99 to get 9(x−4)9(x-4).
  2. Identify Unique Factors: Identify the unique factors in both factored denominators.\newlineThe first denominator has the factors 55 and (x+3)(x+3).\newlineThe second denominator has the factors 99 and (x−4)(x-4).
  3. Determine LCD: Determine the least common denominator (LCD) by taking the product of the unique factors.\newlineThe LCD will be the product of 55, 99, (x+3)(x+3), and (x−4)(x-4).
  4. Write LCD in Factored Form: Write the LCD in factored form.\newlineThe LCD in factored form is 5×9×(x+3)×(x−4)5 \times 9 \times (x+3) \times (x-4).

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