Verify the Equation: Is (3-x)/(-x+3) = 0 Correct?

Q: How can I tell if the numerator and denominator are opposites?

Look for terms that are negatives of each other. Here, 3-x and -x+3 are opposites because if you factor out -1 from the bottom: $ -x+3 = -(x-3) $, and the top is 3-x = -(x-3) too!

Q: Why doesn't this fraction equal zero?

A fraction equals zero only when the numerator is zero and the denominator is non-zero. Since 3-x and -x+3 are opposites (not zero), this fraction equals -1, not 0.

Q: What's the easiest way to simplify fractions with opposite terms?

When you see opposite terms, remember: $ \frac{a}{-a} = -1 $ and $ \frac{-a}{a} = -1 $. The fraction always equals -1 when numerator and denominator are opposites!

Q: Are there any values of x I should avoid?

Yes! Avoid x=3 because it makes the denominator $ -x+3 = -3+3 = 0 $, which makes the fraction undefined. For all other values, the fraction equals 1.

Fraction Simplification with Opposite Terms

Determine if the simplification below is correct:

$\frac{3-x}{-x+3}=0$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine if the reduction is correct

00:03 We'll use the substitution law so the denominator matches the numerator

00:15 We'll reduce what we can, when reducing the entire fraction 1 always remains

00:26 Let's compare the expressions

00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine if the simplification below is correct:

$\frac{3-x}{-x+3}=0$

Step-by-step solution

$\frac{z-x}{-x+z}=1$

Final Answer

Incorrect

Key Points to Remember

Essential concepts to master this topic

Denominator Rule: Notice when numerator and denominator are opposites
Technique: Factor out -1 from (-x+3) to get -(x-3)
Check: $\frac{3-x}{-x+3} = \frac{-(x-3)}{-(x-3)} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Assuming the fraction equals zero
Don't think $\frac{3-x}{-x+3} = 0$ just because it looks complicated! A fraction equals zero only when the numerator is zero and denominator is non-zero. Always recognize that 3-x and -x+3 are opposites, making this fraction equal to -1.

Practice Quiz

Test your knowledge with interactive questions

Determine if the simplification shown below is correct:

$\frac{7}{7\cdot8}=8$

FAQ

Everything you need to know about this question

How can I tell if the numerator and denominator are opposites?

Look for terms that are negatives of each other. Here, 3-x and -x+3 are opposites because if you factor out -1 from the bottom: $-x+3 = -(x-3)$ , and the top is 3-x = -(x-3) too!

Why doesn't this fraction equal zero?

A fraction equals zero only when the numerator is zero and the denominator is non-zero. Since 3-x and -x+3 are opposites (not zero), this fraction equals -1, not 0.

What's the easiest way to simplify fractions with opposite terms?

When you see opposite terms, remember: $\frac{a}{-a} = -1$ and $\frac{-a}{a} = -1$ . The fraction always equals -1 when numerator and denominator are opposites!

How do I check my answer?

Pick any value for x (except x=3 which makes denominator zero) and substitute. Try x=0: $\frac{3-0}{-0+3} = \frac{3}{3} = 1$ . Wait, that's 1, not -1! Let me recalculate: $\frac{3-x}{-x+3} = \frac{3-x}{3-x} = 1$ ✓

Are there any values of x I should avoid?

Yes! Avoid x=3 because it makes the denominator $-x+3 = -3+3 = 0$ , which makes the fraction undefined. For all other values, the fraction equals 1.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Factorization questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime