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Simplify. Express your answer as a single fraction in simplest form. \newlineqr5+q5r44\frac{qr}{5} + \frac{q^5r^4}{4}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlineqr5+q5r44\frac{qr}{5} + \frac{q^5r^4}{4}
  1. Identify Common Denominator: Identify the common denominator for the fractions qr5\frac{qr}{5} and q5r44\frac{q^5r^4}{4}. Since the denominators are 55 and 44, the least common denominator (LCD) is their least common multiple, which is 2020.
  2. Rewrite with Common Denominator: Rewrite each fraction with the common denominator of 2020. For the first fraction, multiply both the numerator and the denominator by 44 to get (4qr)/20(4qr)/20. For the second fraction, multiply both the numerator and the denominator by 55 to get (5q5r4)/20(5q^5r^4)/20.
  3. Combine Fractions: Combine the fractions over the common denominator.\newlineNow that both fractions have the same denominator, we can combine them:\newline(4qr)/20+(5q5r4)/20=(4qr+5q5r4)/20(4qr)/20 + (5q^5r^4)/20 = (4qr + 5q^5r^4)/20
  4. Simplify Expression: Simplify the expression if possible.\newlineIn this case, there are no common factors in the numerator that can be canceled with the denominator, so the expression is already in its simplest form.

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