Simplify. Express your answer as a single fraction in simplest form. \( \frac{10}{2 p-1}-(10 p-7) \)

To simplify the expression \( \frac{10}{2p-1} - (10p - 7) \), we first rewrite it with a common denominator. The first term already has the denominator \( 2p - 1 \), so we need to express the second term with this same denominator: \[ 10p - 7 = \frac{(10p - 7)(2p - 1)}{2p - 1} \] Expanding the numerator: \[ (10p - 7)(2p - 1) = 20p^2 - 10p - 14p + 7 = 20p^2 - 24p + 7 \] Now substitute this back into the expression: \[ \frac{10}{2p - 1} - \frac{20p^2 - 24p + 7}{2p - 1} \] Combine the fractions: \[ \frac{10 - (20p^2 - 24p + 7)}{2p - 1} = \frac{10 - 20p^2 + 24p - 7}{2p - 1} = \frac{-20p^2 + 24p + 3}{2p - 1} \] To write it in standard form, we can move the negative sign: \[ \frac{-1(20p^2 - 24p - 3)}{2p - 1} \] Thus, the simplified expression is: \[ \frac{20p^2 - 24p - 3}{1 - 2p} \] Now, we search for any possible factorization of the numerator but it doesn't simplify further, so the final answer is: \[ \frac{20p^2 - 24p - 3}{1 - 2p} \]