True or False: The least common denominator of each denominator in the following rational expression is (z-4)(z+4)(z-1)(z+1):
8 / z^2+5z+4 = 1 / z-4 + 1 / z-1
I am stuck on this one...
z^2+5z+4 = (z+1)(z+4)
Now you have denominators
(z+1)(z+4), (z-1) and (z-4)
They have no factors in common, so the LCD is the product of all the denominators. The statement is TRUE.
Ok, thank you!
Thus sucks bro
To determine if the given least common denominator (LCD) is correct, we need to find the LCD of the denominators in the rational expression.
Let's start by factoring each denominator:
1. The denominator z^2+5z+4 can be factored as (z+4)(z+1).
2. The denominator of 1/z-4 is already in factored form as z-4.
3. The denominator of 1/z-1 is already in factored form as z-1.
Now, let's determine the LCD. The LCD is the product of all distinct factors raised to their highest power.
In this case, we have:
LCD = (z+4)(z+1)(z-4)(z-1)
Comparing the LCD we obtained with your given LCD (z-4)(z+4)(z-1)(z+1), we can see that they are the same, just in a different order.
Therefore, the statement is true. The least common denominator of each denominator in the given rational expression is indeed (z-4)(z+4)(z-1)(z+1).