True or False: The least common denominator of each denominator in the following rational expression is -2(x-3)(x-1)
: 8 / x^2-4x+3 = 1 / 3-x + 1 / 2
FALSE?
True or False: The least common denominator of each denominator in the following rational expression is -2(x-1)
:
8 / x^2-4x+3 = 1 / 3-x + 1 / 2
FALSE?
Since x^2-4x+3 = (x-3)(x-1)
and (3-x) is just -(x-3)
The LCD is 2(x-3)(x-1)
So, TRUE
Dunno why they included the "-" in the denominator, but it works with or without it.
Similarly, FALSE for the 2nd
The wording is poor. You can't have an LCD for "each" denominator. It takes more than one to have a "common" denominator.
False.
The least common denominator (LCD) is the smallest expression that can be used as a common denominator for all the fractions in the rational expression.
In this case, the denominators are x^2 - 4x + 3, 3 - x, and 2.
To find the LCD, we need to factor each denominator:
x^2 - 4x + 3 = (x - 3)(x - 1)
3 - x = -(x - 3)
2 = 2
The LCD is the product of the highest powers of each factor, so the LCD in this case is -2(x - 3)(x - 1).
Therefore, the statement "The least common denominator of each denominator in the following rational expression is -2(x - 3)(x - 1)" is TRUE.
False.
To find the least common denominator (LCD) of rational expressions, we need to factor the denominators and identify the common factors.
The expression is:
8 / (x^2 - 4x + 3) = 1 / (3 - x) + 1 / 2
Let's factor the denominators:
x^2 - 4x + 3 = (x - 3)(x - 1)
3 - x = -(x - 3)
2 = 2
Now, let's find the lowest common denominator by taking the factors of each denominator without repetition:
LCD = -2(x - 3)(x - 1)
Comparing the LCD we found with the options given, we can see that the correct answer is False.