To find a, b, and c, we can apply the method of partial fractions to the given expression.
First, we write the expression as:
(2x^2 + 7x - 4)/(x - 2) = [(ax + b) + c/(x - 2)]/(x - 2)
Then, we multiply both sides of the equation by (x - 2) to get:
2x^2 + 7x - 4 = (ax + b)(x - 2) + c
Expanding the right side gives:
2x^2 + 7x - 4 = ax^2 - 2abx + 2b + c
Matching coefficients on both sides, we get the following system of equations:
a + 0 + 0 = 2
0 - 2b + 0 = 7
0 + 0 + 1 = -4
Solving this system, we find that a = 2, b = -3.5, and c = 1.
Therefore, the values of a, b, and c in the expression (2x^2 + 7x - 4)/(x - 2) = ax + b + c/(x - 2) are a = 2, b = -3.5, and c = 1.