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Simplify. Write your answer using whole numbers and variables. \newlined9d27d\frac{d}{9d^2 - 7d}

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Q. Simplify. Write your answer using whole numbers and variables. \newlined9d27d\frac{d}{9d^2 - 7d}
  1. Simplify Fraction: Simplify the expression d9d27d\frac{d}{9d^2 - 7d}. First, we need to simplify the fraction by dividing the numerator by the denominator. d9d2\frac{d}{9d^2} simplifies to 19d\frac{1}{9d} because dd in the numerator and one dd in the denominator cancel out.
  2. Combine Terms: Now we have 19d7d\frac{1}{9}d - 7d. To combine these terms, we need a common denominator. Since 7d7d is not a fraction, we can write it as 7d1\frac{7d}{1}.
  3. Find Common Denominator: Find the common denominator for 19d\frac{1}{9d} and 7d1\frac{7d}{1}. The common denominator is 9d9d. We need to adjust the second term to have this common denominator.
  4. Adjust Second Term: Convert 7d1\frac{7d}{1} to have the common denominator 9d9d. To do this, we multiply both the numerator and the denominator by 9d9d\frac{9d}{9d}. 7d1×9d9d=63d29d\frac{7d}{1} \times \frac{9d}{9d} = \frac{63d^2}{9d}
  5. Subtract Terms: Now we have 19d63d29d\frac{1}{9d} - \frac{63d^2}{9d}. We can subtract the second term from the first term because they have the same denominator. 19d63d29d=163d29d\frac{1}{9d} - \frac{63d^2}{9d} = \frac{1 - 63d^2}{9d}
  6. Simplify Numerator: Simplify the numerator 163d21 - 63d^2. The numerator does not simplify further because 11 and 63d263d^2 are not like terms.
  7. Final Expression: Write the final simplified expression.\newlineThe final simplified expression is (163d2)/9d(1 - 63d^2)/9d.

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