X/105-x*5/10=0

To solve the equation \( \frac{x}{105} - \frac{x \cdot 5}{10} = 0 \), we can start by simplifying the equation. 1. First, rewrite the equation: \[ \frac{x}{105} - \frac{5x}{10} = 0 \] 2. Next, simplify \( \frac{5x}{10} \): \[ \frac{5x}{10} = \frac{x}{2} \] So the equation becomes: \[ \frac{x}{105} - \frac{x}{2} = 0 \] 3. Now, find a common denominator to combine the fractions. The least common multiple of \( 105 \) and \( 2 \) is \( 210 \). Rewrite each fraction: \[ \frac{x}{105} = \frac{2x}{210} \] \[ \frac{x}{2} = \frac{105x}{210} \] 4. Substitute these back into the equation: \[ \frac{2x}{210} - \frac{105x}{210} = 0 \] 5. Combine the fractions: \[ \frac{2x - 105x}{210} = 0 \] \[ \frac{-103x}{210} = 0 \] 6. For this fraction to be zero, the numerator must be zero: \[ -103x = 0 \] 7. Solve for \( x \): \[ x = 0 \] Thus, the solution to the equation is: \[ \boxed{0} \]