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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{2}{u^3} + 3t$

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Simplify mixed rational expressions

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

\newline

\frac{2}{u^3} + 3t

Identify Common Denominator: Identify the common denominator for the fractions. $\newline$ Since the first term is a fraction with denominator $u^3$ and the second term is not a fraction, we can consider the second term as a fraction with denominator $1$ . The common denominator for the two terms is $u^3$ .
Express Second Term: Express the second term as a fraction with the common denominator. $\newline$ To do this, we multiply the numerator and denominator of the second term by $u^3$ . This gives us: $\newline$ $3t \times \left(\frac{u^3}{u^3}\right) = \frac{3tu^3}{u^3}$
Combine Fractions: Combine the two fractions over the common denominator. $\newline$ Now we have: $\newline$ $(\frac{2}{u^3}) + (\frac{3tu^3}{u^3})$ $\newline$ Since they have the same denominator, we can combine them into a single fraction: $\newline$ $(\frac{2 + 3tu^3}{u^3})$
Check Simplification: Check if the numerator can be simplified. $\newline$ The numerator $2 + 3tu^3$ does not have any common factors with the denominator $u^3$ , and there are no like terms to combine in the numerator. Therefore, the expression is already in its simplest form.

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