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Simplify. Express your answer as a single fraction in simplest form. \newlinetu4−6tu35\frac{tu}{4} - \frac{6tu^3}{5}

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Add and subtract rational expressionsright chevron icon

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlinetu4−6tu35\frac{tu}{4} - \frac{6tu^3}{5}
  1. Identify Common Denominator: Identify the common denominator for the fractions tu4\frac{tu}{4} and 6tu35\frac{6tu^3}{5}. The common denominator for 44 and 55 is 2020. We will rewrite both fractions with the common denominator of 2020.
  2. Rewrite First Fraction: Rewrite the first fraction tu4\frac{tu}{4} with the common denominator.\newlinetu4=tu×54×5=5tu20\frac{tu}{4} = \frac{tu \times 5}{4 \times 5} = \frac{5tu}{20}
  3. Rewrite Second Fraction: Rewrite the second fraction 6tu35\frac{6tu^3}{5} with the common denominator.\newline6tu35=(6tu3×45×4)=24tu320\frac{6tu^3}{5} = \left(\frac{6tu^3 \times 4}{5 \times 4}\right) = \frac{24tu^3}{20}
  4. Subtract Fractions: Subtract the second fraction from the first fraction.\newline(5tu20)−(24tu320)=5tu−24tu320(\frac{5tu}{20}) - (\frac{24tu^3}{20}) = \frac{5tu - 24tu^3}{20}
  5. Check Simplification: Check if the numerator can be simplified.\newlineThe terms in the numerator, 5tu5tu and 24tu324tu^3, do not have common factors other than tutu, and they are not like terms, so the numerator cannot be simplified further.

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