To evaluate the expression \( \frac{b}{b^2 - c + d} \) for \( b = 3 \), \( c = 2 \), and \( d = -4 \), we first substitute the values into the expression.
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Calculate \( b^2 \): \[ b^2 = 3^2 = 9 \]
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Substitute the values into the denominator: \[ b^2 - c + d = 9 - 2 + (-4) \] \[ = 9 - 2 - 4 \] \[ = 7 - 4 = 3 \]
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Now substitute \( b \) and the simplified denominator into the original expression: \[ \frac{b}{b^2 - c + d} = \frac{3}{3} \]
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Simplify: \[ \frac{3}{3} = 1 \]
Thus, the final simplified answer is \( \boxed{1} \).