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Simplify. Express your answer as a single fraction in simplest form. \newlineqr53−4r\frac{qr^5}{3} - 4r

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Simplify mixed rational expressionsright chevron icon

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlineqr53−4r\frac{qr^5}{3} - 4r
  1. Identify Common Denominator: Identify the common denominator for the fractions in the expression.\newlineSince the first term is already a fraction with a denominator of 33, and the second term is a whole number, we can rewrite the whole number as a fraction with the same denominator of 33 to combine them.
  2. Convert Whole Number to Fraction: Convert the whole number term to a fraction with the same denominator.\newlineTo convert 4r4r to a fraction with a denominator of 33, we multiply it by 33\frac{3}{3}, which is equivalent to 11.\newline4r×(33)=4r×334r \times \left(\frac{3}{3}\right) = \frac{4r \times 3}{3}
  3. Rewrite Expression with Like Denominators: Rewrite the expression with like denominators.\newlineNow we have qr53−(4r×3)3\frac{qr^5}{3} - \frac{(4r \times 3)}{3}, which can be combined because they have the same denominator.
  4. Combine Fractions: Combine the fractions.\newlineSince the denominators are the same, we can combine the numerators.\newlineqr5−(4r×3)3\frac{qr^5 - (4r \times 3)}{3}
  5. Simplify Numerator: Simplify the numerator.\newlineMultiply 4r4r by 33 to get 12r12r.\newlineqr5−12rqr^5 - 12r
  6. Write Final Simplified Expression: Write the final simplified expression as a single fraction.\newlineThe final simplified expression is (qr5−12r)/3(qr^5 - 12r)/3.

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