((1/x)-(1/3))/(x-3)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: ((1/x)-(1/3))/(x-3)

This article will guide you through the steps of simplifying the expression: ((1/x)-(1/3))/(x-3).

Step 1: Finding a Common Denominator for the Numerator

First, we need to find a common denominator for the fractions in the numerator: (1/x) - (1/3). The least common denominator for x and 3 is 3x.

• Rewrite (1/x) as (3/3x)
• Rewrite (1/3) as (x/3x)

Now, the expression becomes: ((3/3x) - (x/3x))/(x-3)

Step 2: Combining the Fractions in the Numerator

Since the fractions in the numerator now have the same denominator, we can combine them:

• ((3-x)/3x) / (x-3)

Step 3: Simplifying the Division

Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as:

• ((3-x)/3x) * (1/(x-3))

Step 4: Factoring and Simplifying

Now, we can factor out a -1 from the numerator of the first fraction:

• ((-1)(x-3)/3x) * (1/(x-3))

The (x-3) terms cancel out, leaving us with:

• (-1/3x)

Conclusion

Therefore, the simplified form of the expression ((1/x)-(1/3))/(x-3) is (-1/3x). Remember that this expression is undefined when x = 0 or x = 3.