Simplify. Write your answer using whole numbers and variables. $\newline$ $\frac{r}{3r^2 - 7r}$

Full solution

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

\newline

\frac{r}{3r^2 - 7r}

Identify Common Factors: Identify the terms in the expression and look for common factors. The expression is $\frac{r}{3r^2} - 7r$ . We can see that $r$ is a common factor in both terms.
Factor Out Common Factor: Factor out the common factor $r$ from both terms. $\newline$ We can factor $r$ out of the numerator to simplify the expression. $\newline$ $r(\frac{1}{3r} - 7)$
Simplify Inside Parentheses: Simplify the expression inside the parentheses. $\newline$ Since $r$ is a common factor, we can cancel one $r$ from the term $\frac{1}{3r}$ . $\newline$ $r\left(\frac{1}{3} - 7\right)$
Perform Subtraction: Perform the subtraction inside the parentheses. $\newline$ Now we subtract $7$ from $\frac{1}{3}$ . $\newline$ $\frac{1}{3} - 7 = \frac{1}{3} - \frac{21}{3} = -\frac{20}{3}$
Multiply by Common Factor: Multiply the result by the common factor $r$ that was factored out. $\newline$ Now we multiply $-\frac{20}{3}$ by $r$ . $\newline$ $r \times \left(-\frac{20}{3}\right) = -\frac{20r}{3}$