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Simplify the complex fraction: (1/a - 1/b) / (1 - ab)

Mathematics

ScanSolve AI Answer

Answer

b−aab−1\frac{b-a}{ab-1}

✅ Correct.

The solution provided in the image correctly simplifies the complex fraction.

Explanation:
The steps shown accurately apply algebraic properties:

  • Multiplicative Identity is used to express terms with a common denominator.
  • The Golden Rule (multiplying numerator and denominator by the same non-zero value) is applied to find common denominators for the sub-fractions.
  • The Distribution Law (factoring out the common denominator 1ab\frac{1}{ab}) is used to combine the terms in the numerator and denominator.
  • Finally, the Cancellation Law is applied to cancel the common factor 1ab\frac{1}{ab} from the main numerator and denominator, leading to the correct simplified form.

The final answer b−aab−1\boxed{\frac{b-a}{ab-1}} is correct.

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