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Simplify. Express your answer as a single fraction in simplest form. \newline29d+4cd4\frac{2}{9d} + \frac{4}{cd^4}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline29d+4cd4\frac{2}{9d} + \frac{4}{cd^4}
  1. Identify LCM: Identify the least common multiple (LCM) of the denominators 9d9d and cd4cd^4. Since 9d9d and cd4cd^4 have no common factors other than dd, the LCM is 9cd49cd^4.
  2. Convert fractions: Convert each fraction to have the LCM as the denominator. For the first fraction, multiply both the numerator and denominator by cd3cd^3 to get (2cd3)/(9cd4)(2cd^3)/(9cd^4). For the second fraction, multiply both the numerator and denominator by 9d39d^3 to get (36d3)/(9cd4)(36d^3)/(9cd^4).
  3. Combine over denominator: Combine the fractions over the common denominator. This gives us (2cd3+36d3)/(9cd4)(2cd^3 + 36d^3)/(9cd^4).
  4. Factor out d3d^3: Simplify the numerator by factoring out the common factor d3d^3. This gives us d3(2c+36)/(9cd4)d^3(2c + 36)/(9cd^4).
  5. Cancel common factor: Simplify the expression by canceling out the common factor of d3d^3 from the numerator and denominator. This results in (2c+36)/(9c)(2c + 36)/(9c).
  6. Add like terms: Simplify the numerator by adding the like terms. This gives us (2c+36)/(9c)=(2c+36c)/(9c)=(38c)/(9c)(2c + 36)/(9c) = (2c + 36c)/(9c) = (38c)/(9c).
  7. Cancel common factor: Cancel the common factor of cc from the numerator and denominator. This results in 389\frac{38}{9}.

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