What is the LCD of these
3m 3n
m+n m-n
(m+n)(m-n)**
2m
2mn
(m-n)^2
What I have so far
1. B
2. C
3. B
4. A
5. D
6. A
7. B
Why did the bicycle fall over? Because it was two-tired from all the LCD calculations!
The least common denominator (LCD) of 3m and 3n is 3mn.
Let's break down the LCD for the given expressions:
- For m+n, the LCD is already 3mn.
- For m-n, the LCD is also 3mn.
So, the LCD for both expressions is 3mn. No fancy tricks needed this time!
To find the least common denominator (LCD) of the given expressions, we need to find the common factors between the denominators.
In this case, the denominators are (m + n) and (m - n). To find the LCD, we need to find the prime factorization of both denominators and take the highest power of each prime factor.
The prime factorization of (m + n) can be written as (m + n).
The prime factorization of (m - n) can be written as (m - n).
Therefore, the LCD of (m + n) and (m - n) is:
(m + n)(m - n)
To find the least common denominator (LCD) for the given expressions, we need to determine the common factors in the denominators and express them in their factored form.
First expression: 3m / (m + n)
Second expression: 3n / (m - n)
Looking at the denominators, we have (m + n) and (m - n). To find the LCD, we need to factorize both expressions.
Factoring (m + n):
The expression (m + n) is already in its factored form, so we don't need to do any further factorization.
Factoring (m - n):
To factor (m - n), we notice that it is in the form of a difference of two squares. We can use the formula (a^2 - b^2) = (a + b)(a - b) to factorize it.
Using this formula, (m - n) = (m + n)(m - n) / (m + n) = (m^2 - n^2) / (m + n)
Now, we have the factors of the denominators:
First expression: 3m / (m + n)
Second expression: 3n / [(m + n)(m - n) / (m + n)]
The next step is to cancel out the common factors. The (m + n) terms cancel out in the second expression, resulting in:
Second expression: 3n / (m - n)
Therefore, the LCD of the given expressions is (m + n)(m - n), or (m^2 - n^2).
strange notation, but correct.
text formatting doesn't work too well here, especially if you omit the horizontal lines. Better just to write
3m/(m+n) and 3n/(m-n)
or even
(3m)/(m+n) and (3n)/(m-n)
in case you make the numerators more complicated later...