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Simplify. Express your answer as a single fraction in simplest form. \newline4q+1q\frac{4}{q} + \frac{1}{q}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline4q+1q\frac{4}{q} + \frac{1}{q}
  1. Identify common denominator: 4q+1q\frac{4}{q} + \frac{1}{q}\newlineIdentify the common denominator.\newlineSince both terms have the same denominator, we can combine them directly.\newline4q+1q=(4+1)q\frac{4}{q} + \frac{1}{q} = \frac{(4 + 1)}{q}
  2. Combine terms: 4q+1q=(4+1)q\frac{4}{q} + \frac{1}{q} = \frac{(4 + 1)}{q}\newlinePerform the addition in the numerator.\newline4+1=54 + 1 = 5\newlineSo, the expression becomes 5q\frac{5}{q}.
  3. Perform addition: 5q\frac{5}{q}\newlineCheck if the fraction can be simplified further.\newlineSince 55 and qq have no common factors other than 11, the fraction is already in its simplest form.

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