Simplify (|x^2|)/(x^2)

Problem

|x^2|/(x^2)

Solution

1. Analyze the expression inside the absolute value. The term x^2 is always non-negative for any real number x because any real number squared is greater than or equal to zero.

2. Apply the definition of absolute value. Since x^2≥0 for all real x the absolute value |x^2| is equal to x^2 itself.

3. Substitute the simplified numerator back into the fraction. This gives (x^2)/(x^2)

4. Simplify the fraction. For all x≠0 the numerator and denominator cancel out to equal 1 Note that the expression is undefined at x=0

Final Answer

|x^2|/(x^2)=1,x≠0

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