Adding Rational Expressions (Unlike Denominators)

Show your work for each problem.

1.
What is the LCD of and ?
1. a)
2. b)
3. c)
4. d)
Answer:
The LCD of and is their product since they share no common factors.
2.
To add and , what must you multiply the first fraction by?
1. a)
2. b)
3. c)
4. d)
Answer:
The first fraction has in the denominator. To get the LCD , multiply by .
3.
Find the LCD of and . (Enter as a power of x)
Answer: x^2
Since contains as a factor, the LCD is (the higher power).
4.
Simplify:
Answer: 2/x
5.
What is the LCD of and ?
1. a)
2. b)
3. c)
4. d)
Answer:
already contains , so the LCD is .
6.
Simplify:
Answer: (3x+1)/(x(x+1))
1. What is the LCD? x(x+1)
2. Rewrite with the LCD. What is the new numerator? x+1
3. Rewrite with the LCD. What is the new numerator? 2x
4. Add the numerators: 3x+1
7.
Simplify and enter only the numerator of the result.
Answer: 2x
. The numerator is .
8.
Simplify:
Answer: (5x+5)/((x+3)(x-2))
1. What is the LCD? (x+3)(x-2)
2. What is ? 2x-4
3. What is ? 3x+9
4. Add: 5x+5
9.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
10.
Simplify:
Answer: (x+1)/((x+3)(x-3))
1. Factor (x+3)(x-3)
2. What is the LCD? (x+3)(x-3)
3. What is ? x-3
4. Add: x+1
11.
Simplify and enter only the numerator.
Answer: 2x+4
12.
Simplify:
Answer: 1
1. Notice that . Rewrite as? -3/(x-3)
2. Now we have . Add the numerators. x-3
3. What is (assuming )? 1
13.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
. So
14.
Simplify:
Answer: (3x+5)/((x+2)(x-2))
1. Factor (x+2)(x-2)
2. What must you multiply by to get the LCD? (x+2)/(x+2)
3. What is ? 2x+4
4. Add the numerators: 3x+5
15.
Simplify:
Answer: (3x^2+6x+2)/(x(x+1)(x+2))
1. What is the LCD of all three fractions? x(x+1)(x+2)
2. What is ? x^2+3x+2
3. What is ? x^2+2x
4. What is ? x^2+x
5. Add all three numerators 3x^2+6x+2
16.
What is the first step when adding and ? (Enter: factor)
Answer: factor
Always factor the denominators first! , which helps find the LCD.
17.
Simplify and state if the result can be reduced:
Answer: (x^2-2x+2)/((x+2)(x-2))
1. Factor (x+2)(x-2)
2. What is the LCD? (x+2)(x-2)
3. Rewrite with the LCD. New numerator? x(x-2)
4. What is ? x^2-2x+2
5. Can the numerator be factored with or ? no