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Simplify. Express your answer as a single fraction in simplest form. \newline4p3+p4\frac{4}{p^3} + \frac{p}{4}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline4p3+p4\frac{4}{p^3} + \frac{p}{4}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators p3p^3 and 44. Since p3p^3 and 44 have no common factors other than 11, the LCM is simply their product, which is 4p34p^3.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 44\frac{4}{4} and the second fraction by p3p3\frac{p^3}{p^3}. This gives us 4×4p3×4+p×p34×p3\frac{4\times 4}{p^3\times 4} + \frac{p\times p^3}{4\times p^3}.
  3. Perform multiplications: Perform the multiplications in the numerators and denominators. This results in 164p3+p44p3\frac{16}{4p^3} + \frac{p^4}{4p^3}.
  4. Add fractions: Add the fractions since the denominators are now the same. The final simplified expression is (16+p4)/(4p3)(16 + p^4)/(4p^3).

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