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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 form of \( \frac{4 x-10}{x-2}-\frac{x-4}{x-2} \) is \(\frac{3x - 6}{x - 2}\)

Step by step solution

01

Identify Common Denominator

Observe that the denominators of both fractions are identical which allows us to proceed to the next step. The denominator is \(x-2\) for both fractions.
02

Combine Numerators

As the fractions already have a common denominator, the subtraction operation is performed in the numerators. The new numerator becomes the result of \( (4x-10) - (x-4)\).
03

Simplify Numerator

Now focus on simplifying the numerator by combining like terms. After subtracting, the numerator simplifies to \(4x - x -10 +4\). Simplify this further to get \(3x - 6\).
04

Write Final Answer

Insert the simplified numerator back into the fraction. The final answer to the problem is \(\frac{3x - 6}{x - 2}\).

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