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Simplifying Complex Fractions in Physics: Methods and Examples

Learn how to simplify complex fractions in physics using different methods with detailed examples and step-by-step solutions. Improve your understanding of lens equation applications.

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Simplifying Complex Fractions in Physics: Methods and Examples

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  1. 1 Lens equation: f = 1 1 + p q EXAMPLE 5 Simplify a complex fraction (Method 1) Physics Let fbe the focal length of a thin camera lens, pbe the distance between an object being photographed and the lens, and q be the distance between the lens and the film. For the photograph to be in focus, the variables should satisfy the lens equation below. Simplify the complex fraction.

  2. 1 1 1 1 1 f = = = + p q q p q + p q + p + pq qp pq pq = EXAMPLE 5 Simplify a complex fraction (Method 1) SOLUTION Write denominator as a single fraction. Divide numerator by denominator.

  3. 5x 3x + 8 5 5 5 x + 4 x + 4 x + 4 1 1 1 2 2 2 + + + x + 4 x + 4 x + 4 x x x = x(x+4) x(x+4) 5x = x + 2(x + 4) = EXAMPLE 6 Simplify a complex fraction (Method 2) Simplify: SOLUTION The LCD of all the fractions in the numerator and denominator is x(x + 4). Multiply numerator and denominator by the LCD. Simplify. Simplify.

  4. – – – 11. 7 7 7 – – – 10 10 10 = – 5x = 3 (2x – 7) 30 30 x x x x x x x x x 6 6 3 5 6 3 5 3 5 for Examples 5 and 6 GUIDED PRACTICE Multiply numberator and denominator by theLCD Simplify

  5. 4 4 4 – – – 12. + + + 3 3 3 = = x x 2 – 4x 2 + 3x 2 (1 – 2x ) 2 2 2 2 2 2 = x x x x x x 2 + 3x for Examples 5 and 6 GUIDED PRACTICE Multiply numberator and denominator by theLCD Simplify Simplify

  6. 3 3 3 x + 5 x + 5 x + 5 13. 2 2 2 1 1 1 + + + x – 3 x – 3 x – 3 x + 5 x + 5 x + 5 = = 3x – 3 3x + 7 3(x – 3) = 3x + 7 (x + 5)(x – 3) (x + 5)(x – 3) for Examples 5 and 6 GUIDED PRACTICE Multiply numberator and denominator by theLCD Simplify Simplify

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