To simplify the expression \( \frac{3}{4} + 3 - \frac{5}{6}r - 6 \), we can follow these steps:
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Combine the constant terms \( 3 \) and \( -6 \): \[ 3 - 6 = -3 \] So, the expression now looks like: \[ \frac{3}{4} - 3 - \frac{5}{6}r \]
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Now, combine \( \frac{3}{4} \) and \( -3 \). We can express \(-3\) with a denominator of 4: \[ -3 = -\frac{12}{4} \] Therefore, \[ \frac{3}{4} - 3 = \frac{3}{4} - \frac{12}{4} = \frac{3 - 12}{4} = \frac{-9}{4} \]
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Now, we substitute \( \frac{-9}{4} \) back into the expression with the term \(- \frac{5}{6}r\): \[ \frac{-9}{4} - \frac{5}{6}r \]
So, the simplified expression is:
\[
\frac{-9}{4} - \frac{5}{6}r
\]
This is the most simplified form of the given expression.