Full solution

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

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\frac{y^3}{5} + 9y

Identify Common Denominator: Identify the common denominator for the two terms in the expression. $\newline$ Since the first term has a denominator of $5$ and the second term can be thought of as having a denominator of $1$ , the common denominator will be $5$ .
Express Second Term: Express the second term with the common denominator. $\newline$ To do this, we multiply both the numerator and the denominator of the second term $9y$ by $5$ . $\newline$ This gives us $(9y \times 5)/(1 \times 5) = 45y/5$ .
Rewrite with Common Denominator: Rewrite the expression with both terms over the common denominator. $\newline$ Now we have $\frac{y^3}{5} + \frac{45y}{5}$ .
Combine Terms: Combine the terms over the common denominator. $\newline$ This gives us $(y^3 + 45y)/5$ .
Check for Simplification: Check if the numerator can be simplified further. $\newline$ In this case, there are no common factors in $y^3$ and $45y$ , so the numerator is already in simplest form.
Write Final Answer: Write the final answer. $\newline$ The expression $y^3/5 + 9y$ simplified as a single fraction in simplest form is $(y^3 + 45y)/5$ .