Question
Simplify. \( -\frac{3 x}{4-x}-\frac{x+4}{x-4} \)
Ask by Collins Hanson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{-2x+4}{4-x} \).
Solution
Calculate or simplify the expression \( -\frac{3x}{4-x}-\frac{x+4}{x-4} \).
Simplify the expression by following steps:
- step0: Solution:
\(-\frac{3x}{4-x}-\frac{x+4}{x-4}\)
- step1: Reduce fractions to a common denominator:
\(-\frac{3x}{4-x}-\frac{\left(x+4\right)\left(-1\right)}{\left(x-4\right)\left(-1\right)}\)
- step2: Reorder the terms:
\(-\frac{3x}{4-x}-\frac{\left(x+4\right)\left(-1\right)}{-\left(x-4\right)}\)
- step3: Rewrite the expression:
\(-\frac{3x}{4-x}-\frac{\left(x+4\right)\left(-1\right)}{4-x}\)
- step4: Transform the expression:
\(\frac{-3x-\left(x+4\right)\left(-1\right)}{4-x}\)
- step5: Multiply the terms:
\(\frac{-3x-\left(-x-4\right)}{4-x}\)
- step6: Subtract the terms:
\(\frac{-2x+4}{4-x}\)
The simplified expression is \( \frac{-2x+4}{4-x} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To simplify the expression \( -\frac{3 x}{4-x}-\frac{x+4}{x-4} \), we first note that \( 4 - x \) can be rewritten as \( -(x - 4) \). Thus, we can write: \[ -\frac{3x}{4-x} = \frac{3x}{x-4} \] Now our expression looks like: \[ \frac{3x}{x-4} - \frac{x+4}{x-4} \] Since both fractions have the same denominator, we can combine them: \[ \frac{3x - (x + 4)}{x-4} \] This simplifies to: \[ \frac{3x - x - 4}{x-4} = \frac{2x - 4}{x-4} \] Next, we can factor out the numerator: \[ \frac{2(x - 2)}{x-4} \] This expression cannot be simplified further, so the final result is: \[ \frac{2(x - 2)}{x - 4} \]
