Simplify. Write your answer using whole numbers and variables. $\newline$ $\frac{m - 6}{m^2 - 6m}$

Full solution

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

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\frac{m - 6}{m^2 - 6m}

Write Expression: Write down the expression to be simplified. $\newline$ The expression given is $m - \frac{6}{m^2 - 6m}.$
Identify Terms: Identify like terms and common factors. $\newline$ In the expression $m - \frac{6}{m^2} - 6m$ , there are no like terms to combine directly. However, we can factor out an $m$ from the terms $m$ and $-6m$ .
Factor Out $m$ : Factor out $m$ from the terms $m$ and $-6m$ . We can write $m - \frac{6}{m^2} - 6m$ as $m(1 - \frac{6}{m^2}) - 6m$ .
Simplify Inside Parentheses: Simplify the expression inside the parentheses. $\newline$ The term $-\frac{6}{m^2}$ can be simplified by multiplying the numerator and denominator by $m^2$ , which gives us $\frac{-6m^2}{m^2}$ .
Perform Division: Perform the division inside the parentheses. $\newline$ Since $-6m^2/m^2$ simplifies to $-6$ , we can rewrite the expression as $m(1 - 6) - 6m$ .
Simplify Inside Parentheses: Simplify the expression inside the parentheses. $1 - 6 = -5$ , so the expression becomes $m(-5) - 6m$ .
Distribute $m$ : Distribute the $m$ across the parentheses. Multiplying $m$ by $-5$ gives us $-5m$ , so the expression is now $-5m - 6m$ .
Combine Like Terms: Combine like terms. $\newline$ $-5m - 6m$ combines to $-11m$ .