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 - 40
c) (x - 1) (x + 4)
d) (x - 1)^2 (x - 4)
did i write it the correct way
-3 / (x^2 - 2x) + 1 /[2x (x^2 - 5x + 4)]
-3/[x(x-2)] + 1/[2x(x-4)(x-1)]
I think maybe a typo
perhaps should be
-3 / (x^2 - 4x) + 1 /[2x (x^2 - 5x + 4)]
-3/[x(x-4)] + 1/[2x(x-4)(x-1)]
multiply top and bottom of first by 2(x-1)
-6(x-1)/[2x(x-4)(x-1)] + 1/[2x(x-4)(x-1)]
[-6x+7]/[2x(x-4)(x-1)]
nope, please check carefully for typos in original.
Yes, you have written the rational expressions correctly. Now, to find the least common denominator (LCD) for the given rational expressions, we need to factor the denominators and find their common factors.
The denominator of the first rational expression is x^2 - 2x. To factor this, we can take out the greatest common factor, which is x, giving us x(x - 2).
The denominator of the second rational expression is 2x (x^2 - 5x + 4). To factor this, we can split the middle term of the quadratic equation and factor it as follows: x^2 - 5x + 4 = (x - 1)(x - 4).
Now, let's gather the common factors from the two denominators:
Common factors:
- x from x(x - 2) in the first expression,
- (x - 1) from (x - 1)(x - 4) in both expressions,
- (x - 4) from (x - 1)(x - 4) in the second expression.
Combining all the common factors, the LCD for the given rational expressions is:
LCD = x(x - 2)(x - 1)(x - 4)
Looking at the answer choices provided:
a) (x - 1)(x - 4)
b) (x - 1)^3(x - 40)
c) (x - 1)(x + 4)
d) (x - 1)^2(x - 4)
None of the answer choices match the LCD we found, which is x(x - 2)(x - 1)(x - 4).