Solve : `(x+3)/(7)-(3x-5)/(5)=(2x-5)/(3)-25`

Answer

To solve the equation \(\frac{x+3}{7} - \frac{3x-5}{5} = \frac{2x-5}{3} - 25\), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM)
The denominators in the equation are 7, 5, and 3. The LCM of these numbers is 105.

### Step 2: Rewrite the Equation
Multiply each term by the LCM (105) to eliminate the fractions:
\[ 105 \left(\frac{x+3}{7}\right) - 105 \left(\frac{3x-5}{5}\right) = 105 \left(\frac{2x-5}{3}\right) - 105 \cdot 25 \]

### Step 3: Simplify Each Term
Calculating each term:
\[ 15(x + 3) - 21(3x - 5) = 35(2x - 5) - 2625 \]
Expanding each term:
\[ 15x + 45 - 63x + 105 = 70x - 175 - 2625 \]

### Step 4: Combine Like Terms
Combine the terms on both sides:
\[ -48x + 150 = 70x - 2800 \]

### Step 5: Move Variables to One Side
Add \(48x\) to both sides and add \(2800\) to both sides:
\[ 150 + 2800 = 70x + 48x \]
This simplifies to:
\[ 2950 = 118x \]

### Step 6: Solve for \(x\)
Now, divide both sides by 118:
\[ x = \frac{2950}{118} \]
Calculating this gives:
\[ x = 25 \]

### Final Answer
The solution to the equation is:
\[ \boxed{25} \]