Find the LCD of the rational expressions.

Help with find the LCD of rational expressions?

  • So I have the problem u^2-2u/u^2-6u+9+4/4u-12. So I was figuring out the LCD and I came out with 4(u-3)^2 but the book says (u-3)^2. What happens to the 4. If you factor them out you ...show more

  • Answer:

    You've written the expression incorrectly. Since you have to write it in one line, it needs parentheses: (u² - 2u)/(u² - 6u + 9) + 4/(4u - 12). Before you calculate the LCD, make sure each fraction is in lowest terms. 4/(4u - 12) = 4/(4(u-3) = 1/(u-3) (u² - 2u)/(u² - 6u + 9) + 4/(4u - 12) = (u² - 2u)/(u-3)² + 1/(u-3) = (u² - 2u)/(u-3)² + (u-3)/(u-3)² The LCD is (u-3)².

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Factor each expression Simplify each expression then look for LCD Note: Domain restrictions are based on the original expression

Mike Brown

[(u^2 - 2u) / (u^2 - 6u + 9)] = u(u - 2) / (u - 3)^2 4 / (4u - 12) = 4 / 4(u - 3) = 1 / (u - 3) [u(u - 2) / (u - 3)^2] + [1 / (u - 3)] LCD is (u - 3)^2 [(u^2 - 2u) / (u - 3)^2] + [(u - 3) / (u - 3)^2] (u^2 - 2u + u - 3) / (u - 3)^2 (u^2 - u - 3) / (u - 3)^2

David

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