Problem 37

Question

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

Step-by-Step Solution

Verified
Answer
The simplified version of the expression is \(\frac{3x - 6}{x - 2}\).
1Step 1: 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: \( (4x-10)-(x-4) \).
2Step 2: 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 \(3x - 6\).
3Step 3: 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 \(\frac{3x - 6}{x - 2}\).