Final answer:
To simplify the expression 2/5m-3/5(2/3m+1), distribute 3/5 across the terms in the parenthesis and cancel out any equivalent terms. The final simplified expression is -3/5, as the terms with variables cancel each other out.
Step-by-step explanation:
To simplify the expression 2/5m-3/5(2/3m+1), we will first distribute the fraction 3/5 across the terms inside the parenthesis:
- Multiply 3/5 by 2/3m to get 6/15m, which simplifies to 2/5m.
- Multiply 3/5 by 1 to get 3/5.
Now, our expression looks like this: 2/5m - 2/5m - 3/5.
Next, we will cancel out the terms 2/5m and -2/5m since they are equivalent but opposite in sign. This leaves us with -3/5. There is no variable to cancel out, as they have already been eliminated. Thus, the simplified expression is just -3/5.
In problems where units (such as meters) are involved, like in the provided reference information, equivalent units in the numerator and denominator cancel out. However, in this algebraic expression, we're dealing with variables and not units of measurement.