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Simplify. Express your answer as a single fraction in simplest form. \newline310bc−5bc5\frac{3}{10bc} - \frac{5}{bc^5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline310bc−5bc5\frac{3}{10bc} - \frac{5}{bc^5}
  1. Identify common denominator: Identify the common denominator.\newlineThe common denominator for the fractions 310bc\frac{3}{10bc} and 5bc5\frac{5}{bc^5} is 10bc510bc^5.
  2. Rewrite fractions: Rewrite each fraction with the common denominator.\newlineFor the first fraction, multiply both the numerator and the denominator by c5c^5 to get 3c510bc5\frac{3c^5}{10bc^5}.\newlineFor the second fraction, multiply both the numerator and the denominator by 1010 to get 5010bc5\frac{50}{10bc^5}.
  3. Combine fractions: Combine the fractions.\newlineNow that both fractions have the same denominator, we can combine them into a single fraction.\newline(3c5)/(10bc5)−(50)/(10bc5)=(3c5−50)/(10bc5)(3c^5)/(10bc^5) - (50)/(10bc^5) = (3c^5 - 50)/(10bc^5)
  4. Simplify numerator: Simplify the numerator if possible.\newlineThe numerator 3c5−503c^5 - 50 cannot be simplified further because there are no common factors between 3c53c^5 and 5050.
  5. Check denominator: Check if the denominator can be simplified.\newlineThe denominator 10bc510bc^5 is already in simplest form because there are no common factors that can be canceled out with the numerator.

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