Multiplying Rational Expressions

Show your work for each problem.

1.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
2.
Simplify: . Enter your answer as a simplified fraction.
Answer: 1
(where )
3.
Which value of would make undefined?
1. a)
2. b)
3. c)
4. d)
Answer:
When , the denominator , which makes the expression undefined.
4.
Simplify: . Enter as a simplified fraction (e.g., 2/3).
Answer: 4/3
(where )
5.
Simplify:
Answer: (x+3)/(x+5)
1. Write the product as a single fraction. What is the numerator? (x+3)(x-2)
2. What is the denominator? (x-2)(x+5)
3. What common factor appears in both numerator and denominator? x-2
4. After canceling, what is the simplified expression? (x+3)/(x+5)
6.
What is in simplified form?
1. a)
2. b)
3. c)
4. d)
Answer:
7.
Simplify: . Enter as a simplified fraction.
Answer: 1/(3x)
where
8.
Simplify:
Answer: x(x-2)
1. Factor (difference of squares) (x+2)(x-2)
2. Factor (common factor) x(x+5)
3. After factoring, which factors cancel? (x+2) and (x+5)
4. What is the final simplified expression? x(x-2)
9.
What are the restrictions on for ?
1. a)
2. b)
3. c)
4. d)
Answer:
The denominators are and . Setting each to zero: and . So .
10.
Simplify: . Enter your answer.
Answer: x-1
where
11.
Simplify:
Answer: x
1. Factor (trinomial) (x-3)(x+2)
2. Factor (difference of squares) (x+3)(x-3)
3. Factor (common factor) x(x+3)
4. Which three factors cancel? (x-3), (x+3), (x+2)
5. What is the final answer? x
12.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
13.
Simplify: . Enter your answer as a simplified expression.
Answer: 1
where
14.
Simplify:
Answer: 2(x+2)/(x+1)
1. Factor completely (factor out 2 first) 2(x+2)(x-2)
2. Factor (x+1)(x+3)
3. Which factors cancel? (x-2) and (x+3)
4. What is the final simplified expression? 2(x+2)/(x+1)
15.
What are ALL the restrictions for ?
1. a)
2. b)
3. c)
4. d)
Answer:
Denominators are and . Setting each factor to zero: . Note: comes from the numerator and doesn't create a restriction.
16.
Simplify:
Answer: x/2
1. Multiply the numerators: ? 5x^2
2. Multiply the denominators: ? 10x
3. Simplify by canceling and x/2