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Chapter 2: Problem 12

Find the key numbers of the expression. $$\frac{x}{x+2}-\frac{2}{x-1}$$

Short Answer

Expert verified
The key numbers of the expression are \(-2\) and \(1\).

Step by step solution

01

Find the Common Denominator

Since these are fractions, the first step is to find a common denominator which allows us to combine the fractions. The denominators here are \(x+2\) and \(x-1\). So, the least common denominator(LCD) is \((x+2)(x-1)\). Multiply both fractions by this common denominator.
02

Simplify

After multiplying both fractions by the common denominator, the expression becomes: \[x(x-1)-(x+2)2 = x^2 - x - 2x - 4\] Then simplify this to \[x^2 - 3x - 4 \]
03

Find the Undefined Values

Now, determine the values for which the original function was undefined. These are the values that make the denominator zero in the original problem. From \(x+2\) and \(x-1\), we can determine that these values are \(-2\) and \(1\).

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