Question
What is the LCD in its factored form of the following rational expression subtraction?
x^2+2x/x^2+7x−8−x/x−1
Responses
x(x+2)
x times open paren x plus 2 close paren -this is the incorrect answer
(x−1)(x+8)
open paren x minus 1 close paren times open paren x plus 8 close paren -this is the correct answer
(x−1)^2(x+8)
open paren x minus 1 close paren squared times open paren x plus 8 close paren -this is the incorrect answer
(x−1)(x^2+7x−8) -this is the incorrect answer
explain how you would get this as your correct answer (x-1)(x+8)
x^2+2x/x^2+7x−8−x/x−1
Responses
x(x+2)
x times open paren x plus 2 close paren -this is the incorrect answer
(x−1)(x+8)
open paren x minus 1 close paren times open paren x plus 8 close paren -this is the correct answer
(x−1)^2(x+8)
open paren x minus 1 close paren squared times open paren x plus 8 close paren -this is the incorrect answer
(x−1)(x^2+7x−8) -this is the incorrect answer
explain how you would get this as your correct answer (x-1)(x+8)
Answers
GPT 3.5
To find the least common denominator (LCD) in this case, you need to factor the denominators of both rational expressions.
For the first rational expression, the denominator is x^2 + 7x - 8, which can be factored as (x - 1)(x + 8).
For the second rational expression, the denominator is x - 1, which is already factored.
To find the LCD, you need to consider the highest power of each factor. In this case, the factors are (x - 1)(x + 8), where (x - 1) has a power of 1 and (x + 8) has a power of 1.
Therefore, the LCD is (x - 1)(x + 8).
For the first rational expression, the denominator is x^2 + 7x - 8, which can be factored as (x - 1)(x + 8).
For the second rational expression, the denominator is x - 1, which is already factored.
To find the LCD, you need to consider the highest power of each factor. In this case, the factors are (x - 1)(x + 8), where (x - 1) has a power of 1 and (x + 8) has a power of 1.
Therefore, the LCD is (x - 1)(x + 8).