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

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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}{tu^4} + \frac{3}{u}

Find Common Denominator: Identify the common denominator for the fractions. $\newline$ Since we have the fractions $\frac{4}{tu^4}$ and $\frac{3}{u}$ , we need to find a common denominator to combine them into a single fraction. The least common denominator (LCD) will be $tu^4$ because it is the least common multiple of $tu^4$ and $u$ .
Rewrite with Common Denominator: Rewrite each fraction with the common denominator. $\newline$ We will rewrite the fraction $\frac{3}{u}$ to have the common denominator $tu^4$ . To do this, we multiply both the numerator and the denominator by $t^3$ . $\newline$ $\frac{4}{tu^4} + \frac{3 \cdot t^3}{u \cdot t^3}$ $\newline$ This gives us: $\newline$ $\frac{4}{tu^4} + \frac{3t^3}{tu^4}$
Combine Fractions: Combine the fractions. $\newline$ Now that both fractions have the same denominator, we can combine them into a single fraction. $\newline$ $(4 + 3t^3)/(tu^4)$
Simplify Expression: Simplify the expression if possible. $\newline$ The expression $(4 + 3t^3)/(tu^4)$ is already in its simplest form. There are no common factors between the numerator and the denominator that can be canceled out.

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