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Simplify. Express your answer as a single fraction in simplest form. \newline2r55+rs4\frac{2r^5}{5} + \frac{rs}{4}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline2r55+rs4\frac{2r^5}{5} + \frac{rs}{4}
  1. Find LCM: Find the least common multiple (LCM) of the denominators 55 and 44. The LCM is 2020.
  2. Make denominators same: Make the denominators the same by multiplying the first fraction by 44 and the second fraction by 55. This gives us (2r5×4)/20+(rs×5)/20(2r^5 \times 4)/20 + (rs \times 5)/20.
  3. Perform multiplication: Perform the multiplication in the numerators. This gives us (8r5)/20+(5rs)/20(8r^5)/20 + (5rs)/20.
  4. Combine fractions: Combine the fractions since the denominators are the same. The combined fraction is (8r5+5rs)/20(8r^5 + 5rs)/20.
  5. Check for simplification: Check if the numerator can be simplified further. Since there are no common factors between 8r58r^5 and 5rs5rs, the numerator cannot be simplified.

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