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Simplify. Express your answer as a single fraction in simplest form. \newline27q5−4q2r\frac{2}{7q^5} - \frac{4}{q^2r}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline27q5−4q2r\frac{2}{7q^5} - \frac{4}{q^2r}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions.\newlineThe LCD for the fractions 27q5\frac{2}{7q^5} and 4q2r\frac{4}{q^2r} is 7q5r7q^5r since it is the smallest expression that both denominators can divide into without leaving a remainder.
  2. Rewrite fractions: Rewrite each fraction with the common denominator.\newlineFor the first fraction, multiply both the numerator and the denominator by rr to get (2r)/(7q5r)(2r)/(7q^5r).\newlineFor the second fraction, multiply both the numerator and the denominator by 7q37q^3 to get (28q3)/(7q5r)(28q^3)/(7q^5r).
  3. Combine fractions: Combine the fractions.\newlineNow that both fractions have the same denominator, we can combine them into a single fraction.\newline(2r)/(7q5r)−(28q3)/(7q5r)=(2r−28q3)/(7q5r)(2r)/(7q^5r) - (28q^3)/(7q^5r) = (2r - 28q^3)/(7q^5r)
  4. Simplify numerator: Simplify the numerator.\newlineSubtract the terms in the numerator to get a single expression.\newline2r−28q3=−28q3+2r2r - 28q^3 = -28q^3 + 2r (rearranging the terms for clarity)
  5. Write final fraction: Write the final simplified fraction.\newlineThe final simplified fraction is (−28q3+2r)/(7q5r)(-28q^3 + 2r)/(7q^5r).

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