Problem 83 - Algebra and Trigonometry

Question

State the name of the property illustrated. $$\frac{1}{(x+3)}(x+3)=1, x \neq-3$$

Step-by-Step Solution

Answer

The property illustrated is 'Any non-zero number divided by itself is 1.'

Step 1: Recognize the Property

Look at the given equation \( \frac{1}{(x+3)}(x+3)=1, x \neq -3 \). Here, we see that \((x+3)\) is divided by itself which results in \(1\). This aligns with the property of any nonzero number divided by itself is \(1\). Remember, \(x\) is not equal to \(-3\) to avoid division by zero.

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Step 6: Conclude with the answer

The property illustrated is 'Any non-zero number divided by itself is 1.'