12. \( \frac{e}{f^{2}-2 f+1} \), for \( e=-6 \) and \( f=5 \) 13. \( \frac{17-u^{2}}{v^{2}-4 v} \), for \( u=-3 \) and \( v=2 \) 14. \( \frac{-50}{2 x^{2}-3 x+5} \), for \( x=-1 \) 15. \( \frac{y^{3}-4 y+6}{3} \), for \( y=-2 \)

Sure, let's evaluate each of the given expressions by substituting the provided values step-by-step. --- ### **Problem 12** \[ \frac{e}{f^{2} - 2f + 1} \] **Given:** \( e = -6 \), \( f = 5 \) **Step 1: Calculate the denominator** \[ f^{2} - 2f + 1 = (5)^{2} - 2(5) + 1 = 25 - 10 + 1 = 16 \] **Step 2: Substitute the values into the expression** \[ \frac{e}{f^{2} - 2f + 1} = \frac{-6}{16} = -\frac{3}{8} \] **Answer:** \(-\frac{3}{8}\) --- ### **Problem 13** \[ \frac{17 - u^{2}}{v^{2} - 4v} \] **Given:** \( u = -3 \), \( v = 2 \) **Step 1: Calculate the numerator** \[ 17 - u^{2} = 17 - (-3)^{2} = 17 - 9 = 8 \] **Step 2: Calculate the denominator** \[ v^{2} - 4v = (2)^{2} - 4(2) = 4 - 8 = -4 \] **Step 3: Substitute the values into the expression** \[ \frac{17 - u^{2}}{v^{2} - 4v} = \frac{8}{-4} = -2 \] **Answer:** \(-2\) --- ### **Problem 14** \[ \frac{-50}{2x^{2} - 3x + 5} \] **Given:** \( x = -1 \) **Step 1: Calculate the denominator** \[ 2x^{2} - 3x + 5 = 2(-1)^{2} - 3(-1) + 5 = 2(1) + 3 + 5 = 2 + 3 + 5 = 10 \] **Step 2: Substitute the values into the expression** \[ \frac{-50}{2x^{2} - 3x + 5} = \frac{-50}{10} = -5 \] **Answer:** \(-5\) --- ### **Problem 15** \[ \frac{y^{3} - 4y + 6}{3} \] **Given:** \( y = -2 \) **Step 1: Calculate the numerator** \[ y^{3} - 4y + 6 = (-2)^{3} - 4(-2) + 6 = -8 + 8 + 6 = 6 \] **Step 2: Substitute the values into the expression** \[ \frac{y^{3} - 4y + 6}{3} = \frac{6}{3} = 2 \] **Answer:** \(2\) --- ### **Summary of Answers** 12. \(-\frac{3}{8}\) 13. \(-2\) 14. \(-5\) 15. \(2\)