(-2/n-6)-(6/2n+3)
To simplify the expression (-2/n-6)-(6/2n+3), we need to find a common denominator and combine the fractions.
Step 1: Find the least common denominator (LCD)
The denominators in the expression are n - 6 and 2n + 3. To find the LCD, we need to factorize these denominators.
n - 6 = 1 * (n - 6)
2n + 3 = 2 * (n + 1.5)
The LCD will be the product of the highest powers of each factor. So, the LCD is 2 * (n - 6) * (n + 1.5).
Step 2: Rewrite the fractions with the LCD as the denominator
Rewrite the first fraction using the LCD:
-2/n-6 = -2 * 2 / (2 * (n - 6) * (n + 1.5))
Rewrite the second fraction using the LCD:
6/2n+3 = (6 * (n - 6)) / (2 * (n - 6) * (n + 1.5))
Step 3: Combine the fractions
Now that both fractions have the same denominator, we can combine them by subtracting the second fraction from the first fraction.
-2 * 2 / (2 * (n - 6) * (n + 1.5)) - (6 * (n - 6)) / (2 * (n - 6) * (n + 1.5))
Simplifying the numerators, we get:
-4 / (2 * (n - 6) * (n + 1.5)) - (6n - 36) / (2 * (n - 6) * (n + 1.5))
Combining the fractions, we have:
(-4 - (6n - 36)) / (2 * (n - 6) * (n + 1.5))
Simplifying further, we get:
(-4 - 6n + 36) / (2 * (n - 6) * (n + 1.5))
Now, we can combine like terms in the numerator:
(-6n + 32) / (2 * (n - 6) * (n + 1.5))
Therefore, the simplified expression is (-6n + 32) / (2 * (n - 6) * (n + 1.5)).