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

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Add and subtract rational expressions

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Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{4}{p^3} + \frac{p}{4}

Find LCM of denominators: Find the least common multiple (LCM) of the denominators $p^3$ and $4$ . Since $p^3$ and $4$ have no common factors other than $1$ , the LCM is simply their product, which is $4p^3$ .
Make denominators the same: Make the denominators the same by multiplying the first fraction by $\frac{4}{4}$ and the second fraction by $\frac{p^3}{p^3}$ . This gives us $\frac{4\times 4}{p^3\times 4} + \frac{p\times p^3}{4\times p^3}$ .
Perform multiplications: Perform the multiplications in the numerators and denominators. This results in $\frac{16}{4p^3} + \frac{p^4}{4p^3}$ .
Add fractions: Add the fractions since the denominators are now the same. The final simplified expression is $(16 + p^4)/(4p^3)$ .

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