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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 is \(\frac{(x-1)}{y x^2}\)

Step by step solution

01

Standardize the Numerator

Make the numerator a single fraction by finding a common denominator which in this case is simply \(x\). This is done through subtracting the fractions: \(1 - \frac{1}{x} = \frac{x}{x} - \frac{1}{x} = \frac{x-1}{x}\). The expression now looks as follows: \(\frac{\frac{x-1}{x}}{x y}\)
02

Simplification

When you divide by a fraction, it's the same as multiplying by its reciprocal. In other words, \((a/b) 梅 (c/d) = (a/b) * (d/c)\). So, our fraction \(\frac{\frac{x-1}{x}}{x y}\) is equivalent to \((\frac{x-1}{x}) * \frac{1}{x y}\), which simplifies to \(\frac{1}{y}\cdot \frac{x-1}{x^2}\)
03

Finalize the expression

Studio the denominator to have only one term, by multiplying the constants and variables separately. The expression becomes \(\frac{(x-1)}{y x^2}\)

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