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Simplify. Express your answer as a single fraction in simplest form. \newline5q4−q2\frac{5q}{4} - \frac{q}{2}

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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. \newline5q4−q2\frac{5q}{4} - \frac{q}{2}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions.\newlineThe denominators are 44 and 22. The LCD of 44 and 22 is 44 because it is the smallest number that both denominators can divide into without a remainder.
  2. Rewrite fractions: Rewrite each fraction with the LCD as the new denominator.\newlineThe first fraction, 5q4\frac{5q}{4}, already has the LCD as its denominator, so it remains unchanged. The second fraction, q2\frac{q}{2}, needs to be rewritten with the LCD as its denominator. To do this, multiply both the numerator and the denominator by 22.\newlineq2=(q×2)(2×2)=2q4\frac{q}{2} = \frac{(q \times 2)}{(2 \times 2)} = \frac{2q}{4}
  3. Combine fractions: Combine the fractions.\newlineNow that both fractions have the same denominator, you can combine them by subtracting their numerators.\newline5q4−2q4=5q−2q4\frac{5q}{4} - \frac{2q}{4} = \frac{5q - 2q}{4}
  4. Simplify numerator: Simplify the numerator.\newlineSubtract the numerators.\newline5q−2q=3q5q - 2q = 3q
  5. Write final answer: Write the final answer.\newlineThe simplified expression is 3q4\frac{3q}{4}.

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