Full solution

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

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

Identify Structure: Identify the structure of the expression. $\newline$ The expression is a fraction with a polynomial in the numerator and a polynomial in the denominator. We need to simplify the expression by combining like terms and reducing the fraction if possible.
Combine Like Terms: Combine like terms in the denominator. $\newline$ The denominator is $d^2 - 6d$ . We can't combine these terms because they are not like terms (one is $d^2$ and the other is $d$ ). So, the denominator remains as it is.
Find Common Factors: Look for common factors in the numerator and the denominator. The numerator is $d - 6$ , and the denominator is $d^2 - 6d$ . We can factor out a $d$ from the denominator to see if it will cancel out with the numerator. $d^2 - 6d = d(d - 6)$
Cancel Common Factors: Cancel out common factors. $\newline$ We now have a common factor of $(d - 6)$ in both the numerator and the denominator. We can cancel this factor out. $\newline$ $\frac{d - 6}{d(d - 6)} = \frac{1}{d}$
Write Final Expression: Write the final simplified expression. $\newline$ After canceling out the common factor, we are left with $\frac{1}{d}$ as the simplified expression.