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Simplify. Express your answer as a single fraction in simplest form. \newline5r+14q5r\frac{5}{r} + \frac{1}{4q^5r}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline5r+14q5r\frac{5}{r} + \frac{1}{4q^5r}
  1. Find LCM: Find the least common multiple (LCM) of the denominators rr and 4q5r4q^5r. Since rr is a factor of 4q5r4q^5r, the LCM is 4q5r4q^5r.
  2. Make denominators same: Make the denominators the same by multiplying the first fraction by 4q54q^5 and the second fraction by 11. This gives us (5×4q5)/(r×4q5)+(1×1)/(4q5r)(5 \times 4q^5)/(r \times 4q^5) + (1 \times 1)/(4q^5r).
  3. Perform multiplication: Perform the multiplication in the numerators. This gives us (20q5)/(4q5r)+1/(4q5r)(20q^5)/(4q^5r) + 1/(4q^5r).
  4. Combine fractions: Combine the fractions since the denominators are the same. The combined fraction is (20q5+14q5r)(\frac{20q^5 + 1}{4q^5r}).
  5. Check for simplification: Check if the fraction can be simplified further. Since 20q520q^5 and 11 have no common factors other than 11, and the denominator 4q5r4q^5r cannot be simplified with the numerator, the fraction is already in simplest form.

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