The fourth degree polynomial equation \(x^4 - 7x^3 + 4x^2 + 7x - 4 = 0\) has four real roots, a, b, c, and d. What is the value of the sum \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}\)? Express your answer as a common fraction.
\(a b c d = c_0 = -4\\ bcd+acd+abd+abc = -(c_1) = -7\\ \dfrac 1 a + \dfrac 1 b+\dfrac 1 c+\dfrac 1 d = \\\dfrac{bcd+acd+abd+abc}{a b c d } = \dfrac{-7}{-4}=\dfrac 7 4\)
\(a b c d = c_0 = -4\\ bcd+acd+abd+abc = -(c_1) = -7\\ \dfrac 1 a + \dfrac 1 b+\dfrac 1 c+\dfrac 1 d = \\\dfrac{bcd+acd+abd+abc}{a b c d } = \dfrac{-7}{-4}=\dfrac 7 4\)
+1242 
