((1/x)-(1/2))/(x-2)

2 min read Jun 16, 2024

Simplifying the Expression ((1/x)-(1/2))/(x-2)

This article will guide you through simplifying the expression ((1/x)-(1/2))/(x-2).

Step 1: Finding a Common Denominator for the Numerator

The first step is to find a common denominator for the fractions in the numerator. The least common multiple of x and 2 is 2x. We can rewrite the expression as follows:

((2/2x)-(x/2x))/(x-2)

Step 2: Combining the Fractions in the Numerator

Now, we can combine the fractions in the numerator:

((2-x)/2x)/(x-2)

Step 3: Simplifying the Complex Fraction

The expression is now a complex fraction. To simplify, we can invert the denominator and multiply:

(2-x)/2x * 1/(x-2)

Step 4: Factoring and Cancelling

Notice that the numerator and denominator share a common factor of (x-2). We can factor out a -1 from the numerator to make this clearer:

(-1(x-2))/2x * 1/(x-2)

Now, we can cancel the (x-2) terms:

(-1)/2x

Conclusion

Therefore, the simplified form of ((1/x)-(1/2))/(x-2) is (-1)/2x, where x ≠ 2. It's important to remember that the expression is undefined when x = 2, as this would result in division by zero.