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)
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).