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Chapter 0: Problem 77

Perform the indicated operations. Simplify the result, if possible. $$\frac{y^{-1}-(y+5)^{-1}}{5}$$

Short Answer

Expert verified
\(\frac{1}{y*(y+5)}\)

Step by step solution

01

Simplify the numerator

To simplify the numerator, first rewrite \(y^{-1}\) and \((y+5)^{-1}\) as \(\frac{1}{y}\) and \(\frac{1}{y+5}\) respectively. Then, find a common denominator to subtract the fractions, which is \(y*(y+5)\). So the new numerator becomes: \(\frac{y+5-y}{y*(y+5)} = \frac{5}{y*(y+5)}\).
02

Simplify the fraction by division

The original fraction is now \(\frac{\frac{5}{y*(y+5)}}{5}\). We simplify this by dividing 5 out from the numerator and denominator which results in \(\frac{1}{y*(y+5)}\).
03

Simplify further

The division can be expressed as multiplication by the reciprocal. So the final answer is \(\frac{1}{y*(y+5)}\).

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