2m + 1
--- ---
6m-3 3-6m
To simplify the expression (2m + 1)/(6m - 3)/(3 - 6m), we can follow these steps:
Step 1: Simplify the numerators and denominators individually.
- Simplify the numerator: (2m + 1)
- Simplify the first denominator: (6m - 3)
- Simplify the second denominator: (3 - 6m)
Step 2: Simplify further if possible.
- Simplify the numerator:
- There is nothing more to simplify in (2m + 1) since it is already in its simplest form.
- Simplify the denominators:
- For (6m - 3), we can factor out a common factor of 3: 3(2m - 1).
- For (3 - 6m), we can factor out a common factor of -3: -3(2m - 1).
So now our expression becomes:
(2m + 1)/(3(2m - 1))/(-3(2m - 1))
Step 3: Simplify further by canceling out common factors.
- We can cancel out the common factor (2m - 1) in the numerator and denominators, leaving us with:
(2m + 1)/3/-3
Step 4: Simplify the remaining expression.
- To divide a fraction by another fraction, you can multiply the first fraction by the reciprocal (or inverse) of the second fraction.
- The reciprocal of -3 is -1/3.
Multiplying (2m + 1)/3 by -1/3, we get:
(2m + 1)/3 * (-1/3) = -(2m + 1)/9
Therefore, the simplified expression is -(2m + 1)/9.