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Simplify. Write your answer using whole numbers and variables. $\newline$ $\frac{d}{9d^2 - 7d}$

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Simplify radical expressions: mixed review

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

\newline

\frac{d}{9d^2 - 7d}

Simplify Fraction: Simplify the expression $\frac{d}{9d^2 - 7d}$ . First, we need to simplify the fraction by dividing the numerator by the denominator. $\frac{d}{9d^2}$ simplifies to $\frac{1}{9d}$ because $d$ in the numerator and one $d$ in the denominator cancel out.
Combine Terms: Now we have $\frac{1}{9}d - 7d$ . To combine these terms, we need a common denominator. Since $7d$ is not a fraction, we can write it as $\frac{7d}{1}$ .
Find Common Denominator: Find the common denominator for $\frac{1}{9d}$ and $\frac{7d}{1}$ . The common denominator is $9d$ . We need to adjust the second term to have this common denominator.
Adjust Second Term: Convert $\frac{7d}{1}$ to have the common denominator $9d$ . To do this, we multiply both the numerator and the denominator by $\frac{9d}{9d}$ . $\frac{7d}{1} \times \frac{9d}{9d} = \frac{63d^2}{9d}$
Subtract Terms: Now we have $\frac{1}{9d} - \frac{63d^2}{9d}$ . We can subtract the second term from the first term because they have the same denominator. $\frac{1}{9d} - \frac{63d^2}{9d} = \frac{1 - 63d^2}{9d}$
Simplify Numerator: Simplify the numerator $1 - 63d^2$ . The numerator does not simplify further because $1$ and $63d^2$ are not like terms.
Final Expression: Write the final simplified expression. $\newline$ The final simplified expression is $(1 - 63d^2)/9d$ .

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