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Chapter 0: Problem 64

Simplify each complex rational expression. $$\frac{1-\frac{1}{x}}{x y}$$

Short Answer

Expert verified
The simplified form of the complex rational expression \(\frac{1-\frac{1}{x}}{xy}\) is \(\frac{1 - \frac{1}{x}}{xy}\).

Step by step solution

01

Simplify the Numerator

First, simplify the numerator which is a fraction. To do this, find a common denominator. Here, it's 'x'. Now, rewrite the numerator as a single fraction by subtracting like terms: \(1-\frac{1}{x}\) can be written as \(\frac{x}{x} - \frac{1}{x}\), which simplifies to \(\frac{x-1}{x}\).
02

Rewrite the Complex Fraction

Next, rewrite the whole complex fraction as \(\frac{\frac{x-1}{x}}{xy}\) which simplifies to \(\frac{x-1}{x^2y}\). This form is easier to manipulate.
03

Simplify the Fraction

Finally, simplify the whole fraction by dividing each term in the numerator by 'x': \(\frac{x-1}{x^2y} = \frac{1 - \frac{1}{x}}{xy}.\)

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