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Simplify. Express your answer as a single fraction in simplest form. \newline2bc4+4c\frac{2}{bc^4} + \frac{4}{c}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline2bc4+4c\frac{2}{bc^4} + \frac{4}{c}
  1. Identify LCM: Identify the least common multiple (LCM) of the denominators bc4bc^4 and cc. Since cc is a factor of bc4bc^4, the LCM is bc4bc^4.
  2. Rewrite fractions: Rewrite each fraction with the LCM as the denominator. To do this, multiply the numerator and denominator of the first fraction by cc and the numerator and denominator of the second fraction by b4c3b^4c^3. This gives us (2c)/(bc4)+(4b4c3)/(bc4)(2c)/(bc^4) + (4b^4c^3)/(bc^4).
  3. Simplify numerators: Simplify the numerators of both fractions. The first fraction remains unchanged as (2c)/(bc4)(2c)/(bc^4). The second fraction simplifies to (4b4c3)/(bc4)(4b^4c^3)/(bc^4) because b4c3b^4c^3 is the result of multiplying 44 by b4c3b^4c^3.
  4. Combine fractions: Combine the fractions now that they have the same denominator. This results in (2c+4b4c3)/(bc4)(2c + 4b^4c^3)/(bc^4).
  5. Factor out common factor: Factor out the common factor of cc from the numerator. This gives us c(2+4b4c2)bc4\frac{c(2 + 4b^4c^2)}{bc^4}.
  6. Cancel common factor: Simplify the fraction by canceling out the common factor of cc from the numerator and denominator. This results in (2+4b4c2)/(b1c3)(2 + 4b^{4}c^{2})/(b^{1}c^{3}).
  7. Write final answer: Write the final simplified expression. The final answer is (2+4b4c2)/(bc3)(2 + 4b^4c^2)/(bc^3).

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