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Simplify. Express your answer as a single fraction in simplest form. \newline5q−q3q\frac{5}{q} - \frac{q^3}{q}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline5q−q3q\frac{5}{q} - \frac{q^3}{q}
  1. Identify common denominator: 5q−q3q\frac{5}{q} - \frac{q^3}{q}\newlineIdentify the common denominator.\newlineSince both terms have the same denominator, we can combine them under one denominator.\newline5q−q3q=5−q3q\frac{5}{q} - \frac{q^3}{q} = \frac{5 - q^3}{q}
  2. Combine terms under denominator: (5−q3)/q(5 - q^3)/q\newlineCheck if the numerator can be factored or simplified further.\newlineThe numerator 5−q35 - q^3 cannot be factored further since it is not a difference of squares or any other factorable form involving qq.
  3. Check for further factorization: (5−q3)/q(5 - q^3)/q\newlineCheck if the fraction can be simplified by canceling common factors.\newlineThere are no common factors between the numerator and the denominator, so the fraction is already in simplest form.

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