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)^3 (x - 4)
c)(x - 1) (x + 4)
d)(x - 1)^2 (x - 4)

-3/[(x-1)(x-1)]

2x/[(x-4)(x-1)]
it has to have (x-4) and two (x-1)s

(-3/(X^2-2X+1))+(2X/(X^2-5X+4)

In order to find an LCD, we need 2 or
more fractions separated by a plus or
minus sign. so I added a plus sign.

CD=(X^2-2X+1)(X^2-5X+4)=(X-1)^2(X-1)(X-4).This product is a CD but not the LCD. To get LCD, reduce the squared factor to (X-1), LCD=(X-1)(X-1)(X-4)=
(X-1)^2(X-4).

To find the least common denominator (LCD) for the given rational expressions, we need to factor the denominators and identify the common factors.

Let's start by factoring the denominators of the given rational expressions:

For the first rational expression, x^2 - 2x + 1, we notice that it is a perfect square trinomial and can be factored as (x - 1)(x - 1) or (x - 1)^2.

For the second rational expression, x^2 - 5x + 4, we can factor it as (x - 1)(x - 4).

Now, we need to identify the common factors among the denominators. In this case, the only common factor is (x - 1).

To find the LCD, we need to take the highest power of each factor.

Since the factor (x - 1) appears squared (i.e., raised to the power of 2) in one denominator and to the first power in the other denominator, we take the highest power, which is (x - 1)^2.

So, the LCD for the given rational expressions is (x - 1)^2 (x - 4).

Therefore, the correct answer is option d) (x - 1)^2 (x - 4).