Problem 59
Question
Simplify each complex rational expression. $$\frac{\frac{x}{3}-1}{x-3}$$
Step-by-Step Solution
Verified Answer
The simplified form of the complex rational expression \(\frac{\frac{x}{3}-1}{x-3}\) is \(\frac{x-3}{3x-9}\)
1Step 1: Identify the LCD
Identify the least common denominator (LCD) of all the fractions in the complex rational expression. In our case, \(\frac{x}{3}\) and \(x-3\) are the fractions. Therefore, the LCD is 3.
2Step 2: Multiply by LCD
Multiply the numerator and the denominator of the complex rational expression by the LCD found in Step 1: \[3 \times (\frac{x}{3}-1)\] \[3 \times (x-3)\]
3Step 3: Simplify the expressions
Simplify the expressions on the top and bottom: \[(x-3)\] \[3x-9\]
4Step 4: Simplify the ratio
Simplify the ratio by cancelling out the common factor between the numerator and the denominator, if any: \[\frac{x-3}{3x-9}\]
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