Finding the LCD of Rational Expressions

Answer: 12

and . LCD .

Answer: x^2

The first denominator has , the second has . The LCD uses the highest power: .

Answer:

Since and share no common factors, the LCD is their product: .

Answer: 6x

and . LCD .

Answer: 24x^2

1. Factor 8 into primes: 2^3
2. Factor 12 into primes: 2^2 * 3
3. What is the LCM of 8 and 12? 24
4. What is the highest power of x needed? x^2
5. What is the complete LCD? 24x^2

Answer:

. Since already appears in the factored form, LCD .

Answer: (x-4)^2

The factor appears to the power 2 in the first denominator and power 1 in the second. Use the highest: .

Answer: (x+1)^2(x-1)

1. Factor : (x+1)(x-1)
2. Factor : (x+1)^2
3. What is the common factor? (x+1)
4. What is the highest power of needed? 2
5. What is the complete LCD? (x+1)^2(x-1)

Answer:

Since , both denominators are really the same factor (differing only by ). The LCD is just .

Answer: x(x+3)(x-3)

1. Factor : x(x+3)
2. Factor : (x+3)(x-3)
3. What factor appears in both? (x+3)
4. List all unique factors: x, (x+3), (x-3)
5. What is the LCD? x(x+3)(x-3)

Answer: (x+2)(x-1)(x+5)

Common factor: . Unique: and . LCD .

Answer: (x-2)^2(x+2)

1. Factor : (x-2)^2
2. Factor : (x+2)(x-2)
3. What is the third denominator? (x+2)
4. What is the highest power of needed? 2
5. What is the complete LCD? (x-2)^2(x+2)

Answer:

and . LCD .

Answer: (x+1)(x+2)(x+3)

and . Common: . LCD .

Answer: 2(x+2)(x-2)^2

1. Factor (first factor out GCF): 2(x+2)(x-2)
2. Factor : (x-2)^2
3. What is the third denominator? (x+2)
4. What is the highest power of ? 2
5. What is the complete LCD? 2(x+2)(x-2)^2

Answer: x^2(x+1)(x-1)

1. Factor : x^2(x-1)
2. Factor : (x+1)(x-1)
3. What is the common factor? (x-1)
4. List all unique factors: x^2, (x+1), (x-1)
5. What is the LCD? x^2(x+1)(x-1)