To divide fractional functions (also known as rational expressions), you essentially "keep, change, flip": keep the first fraction the same, change the division to multiplication, and flip (take the reciprocal of) the second fraction. Then, multiply the numerators and the denominators.
Here's a breakdown:
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Keep: Retain the first fractional function exactly as it is.
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Change: Replace the division symbol (÷) with a multiplication symbol (×).
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Flip: Invert the second fractional function. This means swapping its numerator and denominator. This process is also known as finding the reciprocal.
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Multiply: Multiply the numerators of the two fractions together, and then multiply the denominators of the two fractions together.
Example:
Let's say you want to divide (A/B) by (C/D). Following the steps:
(A/B) ÷ (C/D) = (A/B) × (D/C) = (A×D) / (B×C)
Important Considerations:
- Factoring: Before you multiply, it's often helpful to factor the numerators and denominators of both fractions. This allows you to simplify the expression by canceling out any common factors before multiplying.
- Undefined Values: Remember that the denominator of any fraction cannot be zero. Identify any values that would make the original denominators or the numerator of the flipped fraction equal to zero, as these values are excluded from the domain of the resulting expression.
By following these steps, you can effectively divide fractional functions and simplify the results.
