Subtracting Rational Expressions (Like Denominators)

Show your work for each problem.

1.
What is the first step when subtracting ?
1. a)Multiply the numerators
2. b)Add the denominators
3. c)Verify the denominators are the same
4. d)Factor both expressions
Answer: Verify the denominators are the same
Always verify the denominators are identical before subtracting. Here both have , so we can subtract the numerators directly.
2.
Simplify: . Enter only the numerator of your answer.
Answer: 4x
. The numerator is .
3.
What is equal to?
1. a)
2. b)
3. c)
4. d)
Answer:
. The negative changes both signs: becomes , and becomes .
4.
Simplify:
Answer: 5x/(x+1)
1. What is the common denominator? x+1
2. Subtract the numerators: 5x
3. Write the final answer as a fraction 5x/(x+1)
5.
Simplify: . Enter your answer as a fraction.
Answer: 5/(2x+3)
6.
Simplify:
Answer: (3x+2)/(x-2)
1. Write the subtraction with parentheses: 2x+1
2. Distribute the negative: 1
3. Combine like terms: 3x
4. Combine constants: 2
5. Write the final answer (3x+2)/(x-2)
7.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
. The answer is .
8.
Simplify and factor the numerator. Write your answer in factored form.
Answer: x(x+3)/(x+3)
. This can be simplified to (for ).
9.
Simplify:
Answer: (3x+6)/(x^2-9)
1. Subtract the numerators: 7
2. Combine x terms: 3x
3. Combine constants: 6
4. Write the simplified numerator 3x+6
10.
Simplify and factor: . What is the simplified answer?
Answer: (x+2)/(x+4)
. No common factors to cancel.
11.
What is the result of ?
1. a)
2. b)
3. c)
4. d)
Answer:
When numerators are identical, (where ).
12.
Simplify completely:
Answer: (2x+4)/(x-3)
1. Set up subtraction: . Distribute the negative to get 8
2. Combine terms: 0
3. What remains after combining all terms? 2x+4
4. Write the final answer (2x+4)/(x-3)
13.
Simplify: . Factor your final answer completely.
Answer: (x^2+2x)/(x^2+x)
. So we get (for ).
14.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
. This can also be factored as .
15.
Simplify completely:
Answer: 4/(x-2)
1. Subtract the numerators: 4x+8
2. Factor the numerator 4(x+2)
3. Factor the denominator (x+2)(x-2)
4. Cancel common factors. What remains? 4/(x-2)
16.
If , what is the value of ?
Answer: 7
. For this to equal : , so .