Full solution

Q. Simplify. Write your answer using whole numbers and variables.

\newline

\frac{4g^2 + 9g}{4g + 9}

Identify and Simplify Like Terms: Identify like terms and simplify the expression. $\newline$ The expression given is $4g^2 + \frac{9g}{4g} + 9$ . We can simplify the fraction $\frac{9g}{4g}$ by dividing $9g$ by $4g$ . $\newline$ $\frac{9g}{4g} = \frac{9}{4}$ , since the $g$ terms cancel out.
Rewrite with Simplified Fraction: Rewrite the expression with the simplified fraction. $\newline$ Now we have $4g^2 + \frac{9}{4} + 9$ . Since $\frac{9}{4}$ is not a like term with $4g^2$ or $9$ , we cannot combine them.
Combine Whole Numbers if Possible: Combine the whole numbers if possible. $\newline$ The whole numbers in the expression are $\frac{9}{4}$ and $9$ . We can combine them by converting $9$ to a fraction with the same denominator as $\frac{9}{4}$ . $\newline$ $9 = \frac{36}{4}$ (since $9 \times 4 = 36$ ) $\newline$ Now we can add $\frac{9}{4}$ and $\frac{36}{4}$ .
Add Fractions: Add the fractions. $\newline$ $\frac{9}{4} + \frac{36}{4} = \frac{9 + 36}{4} = \frac{45}{4}$
Write Final Simplified Expression: Write the final simplified expression. $\newline$ The final expression is $4g^2 + \frac{45}{4}$ . This cannot be simplified further since there are no like terms to combine.