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Chapter 0: Problem 37

Add or subtract as indicated. $$\frac{4 x-10}{x-2}-\frac{x-4}{x-2}$$

Short Answer

Expert verified
The simplified version of the expression is \(\frac{3x - 6}{x - 2}\).

Step by step solution

01

Identify and Apply Operation

The operation to perform here is subtraction. Also, since the two fractions have the same denominator, \(x-2\), there is no need to find a common denominator. Simply perform the subtraction operation on the numerators: \( (4x-10)-(x-4) \).
02

Perform Subtraction in the Numerator

Perform the subtraction in the numerator by subtracting each term individually. Subtract the \(x\) term from the \(4x\), and subtract \(-4\) from \(-10\). This gives \(4x - x - 10 + 4\). Simplify this to obtain \(3x - 6\).
03

Write the Final Expression

Retain the common denominator and replace the numerator with the result of the subtraction obtained in Step 2. The final expression is \(\frac{3x - 6}{x - 2}\).

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