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Simplify. Express your answer as a single fraction in simplest form. \newline5q2+3q5\frac{5}{q^2} + \frac{3q}{5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline5q2+3q5\frac{5}{q^2} + \frac{3q}{5}
  1. Find LCD: To combine these fractions, we need a common denominator. The least common denominator (LCD) for q2q^2 and 55 is 5q25q^2.
  2. Rewrite fractions: Rewrite each fraction with the common denominator 5q25q^2. For the first fraction, multiply both the numerator and the denominator by 55: (5×5)/(q2×5)=25/(5q2)(5 \times 5) / (q^2 \times 5) = 25 / (5q^2). For the second fraction, multiply both the numerator and the denominator by q2q^2: (3q×q2)/(5×q2)=3q3/(5q2)(3q \times q^2) / (5 \times q^2) = 3q^3 / (5q^2).
  3. Add fractions: Now, add the two fractions with the common denominator: (255q2)+(3q35q2)(\frac{25}{5q^2}) + (\frac{3q^3}{5q^2}).
  4. Combine numerators: Combine the numerators over the common denominator: (25+3q3)/(5q2)(25 + 3q^3) / (5q^2).
  5. Check for simplification: The expression is now a single fraction, but we need to check if it can be simplified further. Since there are no common factors between the numerator and the denominator, the fraction is already in simplest form.

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