Adding Rational Expressions (Like Denominators)

Show your work for each problem.

1.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
Add the numerators: . Keep the denominator: .
2.
Simplify: . Enter the numerator of your answer.
Answer: 3x+4
The sum is . The numerator is .
3.
What value must NOT equal for the expression ?
1. a)
2. b)
3. c)
4. d)
Answer:
If , then , making the denominator zero. Division by zero is undefined.
4.
Add:
Answer: 1
1. What is the common denominator? x+5
2. Add the numerators: x+5
3. What is when ? 1
5.
What is the denominator in the sum ?
Answer: a+7
The denominator is for both fractions and remains in the sum.
6.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
. The answer is .
7.
Add and simplify:
Answer: 2
1. Add the numerators: 2x+8
2. Factor the numerator 2(x+4)
3. Simplify 2
8.
Simplify: . If the result can be factored as , what is ?
Answer: 0
Trick question! does not factor over real numbers (sum of squares). But if we interpret , then . Over reals, the answer stays .
9.
Add:
1. a)
2. b)
3. c)
4. d)
Answer:
. The result is .
10.
Add:
Answer: (x^2+2x+3)/(x+3)
1. Add the numerators: x^2+2x+3
2. Can be factored? (yes/no) no
3. What is the final answer? (x^2+2x+3)/(x+3)
11.
Simplify completely:
1. a)
2. b)
3. c)
4. d)
Answer:
Wait - let me recalculate. . This doesn't factor nicely. Actually is the correct form, but checking: . Hmm, doesn't share factors with . Let me verify the choices... Actually would require the numerator to be , not . The answer should be which is choice B.
12.
Add and simplify:
Answer: (x^2+4)/((x+2)(x-2))
1. Add the numerators: x^2+4
2. Factor the numerator . What do you get? x^2+4
3. Factor the denominator (x+2)(x-2)
4. What is the simplified result? (x^2+4)/((x+2)(x-2))
13.
Simplify: . Express your answer in lowest terms.
Answer: (4x-3)/((x-3)(x+2))
. The denominator is . Factor numerator: does not share factors. Wait - let me recheck: . Actually , but is not a factor. Hmm, doesn't factor to have or . The answer is .
14.
Add and simplify:
Answer: (x^2+2x+7)/((x+3)(x-2))
1. Add the numerators: x^2+2x+7
2. Factor the denominator (x+3)(x-2)
3. Can the numerator be factored? no
4. What is the final simplified form? (x^2+2x+7)/((x+3)(x-2))
15.
For which value of does ?
1. a)
2. b)
3. c)
4. d)
Answer:
. For this to equal , we need , so .
16.
Add:
Answer: 2/(2x-1)
1. What is ? 2
2. What is the denominator? 2x-1
3. Write the final answer 2/(2x-1)