find the lcd of this rational algebraic expression 3x+2,2x/x^2-4,x+1/x^2+5x+6 please answer it immidiately i need the answer as soon as possible ..please?
You have listed three "rational algebraic expressions", not one.
Note that
(x+1)/(x^2+5x+6) = 1/(x+5)
and
2x/(x^2-4) = 2x/[(x+2)(x-2)]
If you really want a least common denominator, it would be
[x+2)(x-2)(x+5)
To find the lowest common denominator (LCD) of the rational algebraic expression 3x + 2, 2x/(x^2 - 4), and (x + 1)/(x^2 + 5x + 6), follow these steps:
Step 1: Factorize the denominators:
(x^2 - 4) = (x + 2)(x - 2)
(x^2 + 5x + 6) = (x + 3)(x + 2)
Step 2: Identify the unique factors with the highest power:
The factors with the highest power for the two expressions are (x + 2) and (x + 3).
Step 3: Multiply all the unique factors with the highest powers:
(x + 2) * (x + 3) = x^2 + 5x + 6
Therefore, the LCD of the given rational algebraic expression is x^2 + 5x + 6.
To find the least common denominator (LCD) of the given rational algebraic expression, we need to factor the denominators and find the common factors.
1. Factor the denominators:
a) For the expression 2x/(x^2 - 4), we observe that the denominator is a difference of squares and can be factored as (x - 2)(x + 2).
b) For the expression x + 1/(x^2 + 5x + 6), we can factor the denominator as (x + 2)(x + 3).
2. Determine the common factors:
The common factors among the two denominators are (x - 2), (x + 2), (x + 3).
3. Compute the LCD:
To find the least common denominator, we multiply all the common factors together:
LCD = (x - 2) * (x + 2) * (x + 3)
Therefore, the least common denominator (LCD) of the rational algebraic expression 3x + 2, 2x/(x^2 - 4), x + 1/(x^2 + 5x + 6) is (x - 2)(x + 2)(x + 3).