(2) \( \frac{25-2 x+1 \times 5 \frac{x}{2}}{125 x-1}=1 \)

To solve the equation \( \frac{25 - 2x + 1 \times 5 \frac{x}{2}}{125x - 1} = 1 \), let's first simplify the numerator. We have: \( 1 \times 5 \frac{x}{2} = \frac{5x}{2} \). Now substituting this into the equation, we have: \( \frac{25 - 2x + \frac{5x}{2}}{125x - 1} = 1 \). Next, combine the terms in the numerator: To combine \( -2x + \frac{5x}{2} \), we convert \( -2x \) into a fraction: \( -2x = -\frac{4x}{2} \). Now we can combine: \( -\frac{4x}{2} + \frac{5x}{2} = \frac{1x}{2} = \frac{x}{2} \). So now the numerator becomes: \( 25 + \frac{x}{2} \). Therefore, our equation simplifies to: \( \frac{25 + \frac{x}{2}}{125x - 1} = 1 \). Now, to eliminate the fraction, we can multiply both sides by \( 125x - 1 \) (assuming \( 125x - 1 \neq 0 \)): \( 25 + \frac{x}{2} = 125x - 1 \). Next, we can eliminate the fraction by multiplying the whole equation by 2: \( 50 + x = 250x - 2 \). Now, let's bring \( x \) terms to one side and constants to the other side: \( 50 + 2 = 250x - x \), This simplifies to: \( 52 = 249x \). Finally, we can solve for \( x \): \( x = \frac{52}{249} \). Thus, the solution to the equation is: \( x = \frac{52}{249} \).