1. EXAMPLE 5 Simplify a complex fraction (Method 1) Let f be the focal length of a thin camera lens, p be 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. Physics Lens equation: f 1 1 p 1 q + =

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

3. EXAMPLE 6 Simplify a complex fraction (Method 2) Simplify: 5 x + 4 1 + 2 x SOLUTION The LCD of all the fractions in the numerator and denominator is x(x + 4). 5 x + 4 1 + 2 x 5 1 + 2 x = x(x+4) Multiply numerator and denominator by the LCD. x + 2(x + 4) 5x5x = Simplify. 5x5x 3x + 8 =

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

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

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