Dividing Rational Expressions

Show your work for each problem.

1.
What is the first step when dividing ?
1. a)Cross multiply
2. b)Multiply by the reciprocal of the second fraction
3. c)Find a common denominator
4. d)Add the numerators
Answer: Multiply by the reciprocal of the second fraction
To divide fractions, we multiply by the reciprocal of the divisor. So .
2.
What is the reciprocal of ? (Write as a fraction like 5/3)
Answer: 5/3
The reciprocal of is . We simply flip the fraction, swapping numerator and denominator.
3.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
. The terms cancel out.
4.
Simplify: (Enter the simplified coefficient only)
Answer: 4
. The coefficient is .
5.
Which values must be excluded from the domain of ?
1. a)
2. b)
3. c)
4. d)No excluded values
Answer:
After flipping: . The in the denominator means . The final answer is , but must still be excluded.
6.
Divide and simplify:
Answer: x + 2
1. Rewrite as multiplication. What is the reciprocal of ? (x+3)/(x-2)
2. Factor . What is its factored form? (x+2)(x-2)
3. After canceling and , what remains? x+2
7.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
, where .
8.
Simplify . Enter the answer in factored form.
Answer: x+1
, where .
9.
Divide:
Answer: 1
1. Factor (x+2)(x+3)
2. Factor (x+2)(x-2)
3. Multiply by reciprocal and cancel. What is the final simplified answer? 1
10.
What are ALL the excluded values for ?
1. a)
2. b)
3. c)
4. d)
Answer:
From : . From : . From (becomes denominator after flip): .
11.
Divide and simplify:
Answer: (x+1)/(x-1)
1. Factor (2x-3)(x+1)
2. Factor (x+1)(x-1)
3. Rewrite as multiplication and cancel. What is the final answer? (x+1)/(x-1)
12.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
, where .
13.
Simplify: . Enter the numerator of the simplified answer.
Answer: x+4
. Wait - actually the answer is . Let me recalculate: . The numerator is before final cancellation, so answer is .
14.
Divide:
Answer: (x+5)/(x+3)
1. Factor (x+5)(x+1)
2. Factor (x+3)(x+1)
3. Simplify 1
4. What is ? (x+5)/(x+3)
15.
Simplify:
Answer: 1
1. Factor using difference of cubes: (x-2)(x^2+2x+4)
2. Factor (x+2)(x-2)
3. Multiply by reciprocal and simplify. What is the final answer? 1