what's the least common denominator that can be used to solve: 1/x + 2/(x-3) = 5
x(x-3)
To find the least common denominator for the given equation, we need to determine the least common multiple (LCM) of the denominators of the two fractions.
The denominators in this equation are x and x-3.
Step 1: Factorize the denominators
x cannot be factorized further.
(x-3) is already in the simplest form.
Step 2: Identify the common and unique factors from the factorized denominators
Since the denominators do not have any common factors, we consider them both as unique factors.
Step 3: Determine the LCM by multiplying the common and unique factors
LCM = x * (x - 3)
Therefore, the least common denominator for the given equation is x * (x - 3).
To find the least common denominator (LCD) in this equation, we need to look at the denominators of the given terms, which are x and (x - 3).
The LCD is the smallest expression that both denominators can divide evenly. In this case, the LCD is the product of the denominators since neither of them can be further simplified.
Therefore, the LCD for 1/x and 2/(x - 3) is given by the expression x * (x - 3).
Now, we can solve the equation:
1/x + 2/(x - 3) = 5
To eliminate the fractions, we need to multiply every term in the equation by the LCD:
(x * (x - 3)) * (1/x) + (x * (x - 3)) * (2/(x - 3)) = (x * (x - 3)) * 5
Simplifying this equation will allow us to solve for x.