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Simplify. Write your answer using whole numbers and variables. $\newline$ $\frac{2r^2 + 5r}{2r + 5}$

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Multiply and divide powers: variable bases

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

\newline

\frac{2r^2 + 5r}{2r + 5}

Identify Terms: Identify the terms in the numerator and the denominator. $\newline$ The numerator is $2r^2 + 5r$ , and the denominator is $2r + 5$ .
Factor Out Common Factor: Factor out the greatest common factor in the numerator. $\newline$ The greatest common factor of $2r^2$ and $5r$ is $r$ . So we factor $r$ out of the numerator. $\newline$ $2r^2 + 5r = r(2r + 5)$
Observe for Common Factors: Observe the numerator and the denominator for common factors. The numerator is now $r(2r + 5)$ , and the denominator is $2r + 5$ . We can see that $2r + 5$ is a common factor.
Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. $\newline$ Since $2r + 5$ is present in both the numerator and the denominator, we can cancel it out. $\newline$ $\frac{r(2r + 5)}{2r + 5} = r$
Write Final Expression: Write the final simplified expression. $\newline$ The simplified expression is $r$ .

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