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

Q: Why doesn't this fraction equal zero like I thought?

A fraction only equals zero when the numerator is zero and the denominator is non-zero. Here, both numerator and denominator are the same expression, so we use the rule $ \frac{a}{a} = 1 $ instead!

Q: How can I remember when a fraction equals 1?

Think of simple examples: $ \frac{5}{5} = 1 $, $ \frac{100}{100} = 1 $. The same rule applies to algebraic expressions: identical non-zero numerator and denominator always equal 1.

Q: Is there ever a case where this type of fraction could equal zero?

Never! For any fraction to equal zero, only the numerator can be zero while the denominator must be non-zero. When numerator and denominator are identical, they're either both zero (undefined) or both non-zero (equals 1).

Q: What's the difference between undefined and zero?

Zero is a number you can work with mathematicallyUndefined means the expression has no mathematical meaning and cannot be calculatedThink of it like dividing by zero on a calculator - you get an error, not zero!

Rational Expressions with Common Factors

Determine if the simplification described below is correct:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's check if we reduced correctly.

00:17 When we simplify, remember, the fraction becomes 1 when fully reduced.

00:24 Now, let's compare both expressions to see if they're the same.

00:32 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine if the simplification described below is correct:

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

Step-by-step solution

To determine if the simplification $\frac{x+3}{x+3} = 0$ is correct, we'll consider the mathematical properties of division:

Step 1: Recognize that for any non-zero number $a$ , $\frac{a}{a} = 1$ . This is a fundamental rule of arithmetic for non-zero values.
Step 2: Apply this property to the given expression. Here, $x+3$ is considered as $a$ , leading to $\frac{x+3}{x+3} = 1$ , assuming $x+3$ is not zero.
Step 3: Evaluate the condition when $x = -3$ . If $x = -3$ , then $x+3 = 0$ , making the expression $\frac{0}{0}$ , which is undefined in mathematics.
Step 4: The result $0$ is incorrect because the expression simplifies to $1$ for values where $x+3 \neq 0$ .

Conclusively, the statement $\frac{x+3}{x+3} = 0$ is mathematically incorrect as it defies basic division laws unless in the undefined case.

Therefore, the simplification is incorrect.

Final Answer

Incorrect

Key Points to Remember

Essential concepts to master this topic

Rule: Any non-zero number divided by itself equals 1
Technique: Simplify $\frac{x+3}{x+3} = 1$ when x ≠ -3
Check: Verify domain restrictions: x = -3 makes expression undefined ✓

Common Mistakes

Avoid these frequent errors

Thinking any fraction equals zero
Don't assume $\frac{x+3}{x+3} = 0$ because numerator and denominator look similar! This ignores the fundamental rule that any non-zero number divided by itself equals 1, not 0. Always apply the division rule: $\frac{a}{a} = 1$ when a ≠ 0.

Practice Quiz

Test your knowledge with interactive questions

Determine if the simplification below is correct:

$\frac{3\cdot7}{7\cdot3}=0$

FAQ

Everything you need to know about this question

Why doesn't this fraction equal zero like I thought?

A fraction only equals zero when the numerator is zero and the denominator is non-zero. Here, both numerator and denominator are the same expression, so we use the rule $\frac{a}{a} = 1$ instead!

What happens when x = -3?

When x = -3, both the numerator and denominator become zero, creating $\frac{0}{0}$ , which is undefined in mathematics. The expression simply doesn't exist at this point.

How can I remember when a fraction equals 1?

Think of simple examples: $\frac{5}{5} = 1$ , $\frac{100}{100} = 1$ . The same rule applies to algebraic expressions: identical non-zero numerator and denominator always equal 1.

Is there ever a case where this type of fraction could equal zero?

Never! For any fraction to equal zero, only the numerator can be zero while the denominator must be non-zero. When numerator and denominator are identical, they're either both zero (undefined) or both non-zero (equals 1).

What's the difference between undefined and zero?

Zero is a number you can work with mathematically
Undefined means the expression has no mathematical meaning and cannot be calculated

Think of it like dividing by zero on a calculator - you get an error, not zero!

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