1. Warm up 1. 2. Factor the expression. 10x – 5x2 ANSWER 5x (2 – x)

2. 3. 4. Lesson 8.4, For use with pages 573-580 Factor the expression.
ANSWER
(x – 5)(x2 + 5x + 25) 4.
What is the volume and surface area of a cardboard shipping carton that measures 15 inches by 18 inches by 20 inches?
ANSWER
5400 in.3, 1860 in.2

9. 8.5 – Adding and Subtracting Rational Expressions

10. Add numerators and simplify result.
EXAMPLE 1
Add or subtract with like denominators
Perform the indicated operation. 7 4x + 3 a. 2x
x + 6 – 5 b.
SOLUTION 7 4x + 3 a. =
7 + 3 4x 10 4x = 5 2x =
Add numerators and simplify result. 2x
x + 6 5 – b.
x + 6
2x – 5 =
Subtract numerators.

11. Subtract numerators and simplify results .
GUIDED PRACTICE
for Example 1
Perform the indicated operation and simplify. a. 7
12x + 5 =
7 – 5
12x = 2
12x = 1 6x
Subtract numerators and simplify results . b. 2
3x2 + 1 =
2 + 1
3x2 = 3
3x2 = 1 x2
Add numerators and simplify results. c. 4x
x–2 – x =
4x–x
x–2 = 3x
x–2 = 3x
3x – 2
Subtract numerators.

12. EXAMPLE 2
Find a least common multiple (LCM)
Find the least common multiple of 4x2 –16 and 6x2 –24x + 24.
Factor each polynomial. Write numerical factors as products of primes.

13. EXAMPLE 3
Add with unlike denominators
Add:
9x2 7 + x
3x2 + 3x
SOLUTION

14. EXAMPLE 4
Subtract with unlike denominators
Subtract:
x + 2
2x – 2
–2x –1
x2 – 4x + 3 –
SOLUTION

15. GUIDED PRACTICE
for Examples 2, 3 and 4
Find the least common multiple of the polynomials.
5. 5x3 and 10x2–15x

16. GUIDED PRACTICE
for Examples 2, 3 and 4
Find the least common multiple of the polynomials.
6. 8x – 16 and 12x2 + 12x – 72

17. GUIDED PRACTICE
for Examples 2, 3 and 4 4x 3 – 7 1 7.
SOLUTION

18. GUIDED PRACTICE
for Examples 2, 3 and 4 1
3x2 + x
9x2 – 12x 8.

19. GUIDED PRACTICE
for Examples 2, 3 and 4 x
x2 – x – 12 + 5
12x – 48 9.
SOLUTION

20. Add numerators Simplify GUIDED PRACTICE for Examples 2, 3 and 4
12x + 5x + 15
12(x + 3)(x – 4) =
Add numerators
17x + 15
12(x +3)(x + 4) =
Simplify

21. GUIDED PRACTICE
for Examples 2, 3 and 4
x + 1
x2 + 4x + 4 – 6
x2 – 4
10.
SOLUTION

22. EXAMPLE 5
Simplify a complex fraction (Method 1)
Physics
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.
Lens equation: f 1 p q + =

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

24. GUIDED PRACTICE
for Examples 5 and 6 2 x – + 4 3
12.

25. GUIDED PRACTICE
for Examples 5 and 6 3
x + 5 2
x – 3 + 1
13.