To evaluate the expression \( 9 + (-\frac{3}{4} + 1.25) - 6 \), we can follow these steps:
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Convert 1.25 to a fraction: \[ 1.25 = \frac{5}{4} \]
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Combine the fractions: We need to add \(-\frac{3}{4}\) and \(\frac{5}{4}\): \[ -\frac{3}{4} + \frac{5}{4} = \frac{-3 + 5}{4} = \frac{2}{4} = \frac{1}{2} \]
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Substituting back into the expression: Now replace \(-\frac{3}{4} + 1.25\) with \(\frac{1}{2}\) in the original expression: \[ 9 + \frac{1}{2} - 6 \]
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Evaluate \(9 - 6\): \[ 9 - 6 = 3 \]
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Add \(\frac{1}{2}\): \[ 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \]
Thus, the value of the expression \( 9 + (-\frac{3}{4} + 1.25) - 6 \) is: \[ \boxed{\frac{7}{2}} \]