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Simplify. Express your answer as a single fraction in simplest form. \newline8y53+xy44\frac{8y^5}{3} + \frac{xy^4}{4}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline8y53+xy44\frac{8y^5}{3} + \frac{xy^4}{4}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators 33 and 44. The LCM of 33 and 44 is 1212.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 44 and the second fraction by 33. This gives us (8y5×4)/12+(xy4×3)/12(8y^5 \times 4)/12 + (xy^4 \times 3)/12.
  3. Perform numerator multiplication: Perform the multiplication in the numerators. This results in (32y5)/12+(3xy4)/12(32y^5)/12 + (3xy^4)/12.
  4. Combine fractions with same denominator: Combine the fractions since the denominators are the same. The combined fraction is (32y5+3xy412)(\frac{32y^5 + 3xy^4}{12}).
  5. Check for further simplification: Check if the fraction can be simplified further. In this case, there are no common factors between the numerator and the denominator, so the fraction is already in simplest form.

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