Find the LCD for the following rational expressions.
-3 / x^2 - 2x + 1 2x / x^2 - 5x + 4
a)(x - 1) (x + 4)
b)(x - 1)^2 (x - 4)
c)(x - 1)^3 (x -4)
d)( x - 1) (x - 4)
To find the least common denominator (LCD) for the given rational expressions, you need to factor the denominators of both expressions and then find the product of the highest powers of all the factors.
First, let's factor the denominators of both rational expressions.
For the first rational expression: x^2 - 2x + 1
This is a perfect square trinomial and can be factored as: (x - 1)^2
For the second rational expression: x^2 - 5x + 4
This can be factored as: (x - 1)(x - 4)
Since (x - 1) is a common factor in both denominators, we only need to consider the highest power of each remaining factor. In this case, the highest power of (x - 1) is 2, and the highest power of (x - 4) is 1.
To find the LCD, we take the product of the highest powers of all the factors. Therefore, the LCD is: (x - 1)^2 (x - 4)
So the answer is option b) (x - 1)^2 (x - 4).