## Solving the Equation: (m-3)/2-(2m+1)/3+m/5+3=2m-1/3

This article will guide you through the steps of solving the equation **(m-3)/2-(2m+1)/3+m/5+3=2m-1/3**.

### Step 1: Find a Common Denominator

The first step is to find a common denominator for all the fractions in the equation. The least common multiple of 2, 3, and 5 is 30.

- Multiply the first fraction by 15/15:
**(m-3)/2 * (15/15) = (15m-45)/30** - Multiply the second fraction by 10/10:
**(2m+1)/3 * (10/10) = (20m+10)/30** - Multiply the third fraction by 6/6:
**m/5 * (6/6) = (6m)/30**

Now the equation looks like this:

**(15m-45)/30 - (20m+10)/30 + (6m)/30 + 3 = (2m-1)/3**

### Step 2: Simplify the Equation

- Combine the fractions on the left side of the equation:
**(15m - 45 - 20m - 10 + 6m)/30 + 3 = (2m-1)/3** - Simplify the numerator:
**(m-55)/30 + 3 = (2m-1)/3**

### Step 3: Eliminate Fractions

- Multiply both sides of the equation by 30:
**(m-55) + 90 = 10(2m-1)** - Distribute on the right side:
**(m-55) + 90 = 20m - 10**

### Step 4: Isolate the Variable

- Subtract m from both sides:
**-55 + 90 = 19m - 10** - Add 10 to both sides:
**35 = 19m** - Divide both sides by 19:
**m = 35/19**

### Solution

The solution to the equation is **m = 35/19**.