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Chapter 0: Problem 78

Perform the indicated operations. Simplify the result, if possible. $$\frac{y^{-1}-(y+2)^{-1}}{2}$$

Short Answer

Expert verified
The simplified form of the given expression is \(-\frac{1}{y(y+2)}\).

Step by step solution

01

Consolidate the terms in the numerator

First, we need to consolidate the terms in the numerator. As subtraction is involved, first find a common denominator for the two fractions, which will be \( y \cdot (y+2) \). So the fraction transforms to: \[ \frac{y - (y+2)}{2y(y+2)} \]
02

Simplify the numerator

Simplify the numerator by performing the subtraction. This gives: \[\frac{y - y - 2}{2y(y+2)}\] Simplify to: \[\frac{- 2}{2y(y+2)}\]
03

Simplify the fraction

Continue simplifying the fraction by canceling out the common factors in the numerator and denominator. This will give: \[\frac{-1}{y(y+2)}\]

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