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Answer
The simplified form is \( \frac{x+3}{-3} \).
Solution
Calculate or simplify the expression \( (x+3)(x-4)/(3*(4-x)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(x+3\right)\left(x-4\right)}{\left(3\left(4-x\right)\right)}\)
- step1: Remove the parentheses:
\(\frac{\left(x+3\right)\left(x-4\right)}{3\left(4-x\right)}\)
- step2: Simplify:
\(\frac{\left(x+3\right)\left(x-4\right)}{12-3x}\)
- step3: Multiply the terms:
\(\frac{x^{2}-x-12}{12-3x}\)
- step4: Calculate:
\(\frac{\left(x+3\right)\left(x-4\right)}{-3\left(x-4\right)}\)
- step5: Reduce the fraction:
\(\frac{x+3}{-3}\)
The simplified form of the expression \( \frac{(x+3)(x-4)}{3(4-x)} \) is \( \frac{x+3}{-3} \).
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Simplify this solution Extra Insights
To simplify the expression \( \frac{(x+3)(x-4)}{3(4-x)} \), we recognize that \( 4 - x \) can be rewritten as \( -(x - 4) \). This allows us to rephrase the denominator as \( 3(4-x) = -3(x-4) \). Therefore, the expression simplifies to: \[ \frac{(x+3)(x-4)}{-3(x-4)} \] As long as \( x \neq 4 \) (to avoid division by zero), we can cancel \( (x-4) \) from the numerator and the denominator, which leaves us with: \[ \frac{(x+3)}{-3} = -\frac{x+3}{3} \] So, the simplified expression is: \(-\frac{x+3}{3}\) (for \( x \neq 4 \)).
