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Simplify. Express your answer as a single fraction in simplest form. \newline8xy55+xy5\frac{8xy^5}{5} + \frac{xy}{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. \newline8xy55+xy5\frac{8xy^5}{5} + \frac{xy}{5}
  1. Identify Common Denominator: Identify the common denominator in the fractions 8xy55\frac{8xy^5}{5} and xy5\frac{xy}{5}. Since both fractions have the same denominator, which is 55, we do not need to find a least common multiple (LCM). The common denominator is already 55.
  2. Add Numerators: Add the numerators of the fractions while keeping the common denominator the same. \newline8xy5+xy5\frac{8xy^5+xy}{5}
  3. Factor Out Common Factor: Factor out the common factor xyxy from the numerator. \newline xy(8y4+1)5\frac{xy(8y^4 + 1)}{5}
  4. Check for Further Simplification: Check if the expression can be simplified further. Since there are no common factors between the numerator and the denominator, and the expression inside the parentheses cannot be factored further, the expression is already in its simplest form.

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