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

Determine if the simplification described below is correct:

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

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.