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Chapter 0: Problem 87

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

Short Answer

Expert verified
The simplified form of the provided expression is \(\frac{1}{y(y + 5)}\).

Step by step solution

01

Identify the Common Denominator

Identify the common denominator for \(y\) and \(y + 5\). Since they are both denominators in fractional form, the common denominator would be the product of both which is \(y(y + 5)\).
02

Simplify the Numerator

Rewrite each fraction with the common denominator and subtract. The numerator now becomes \((y + 5) - y\), which simplifies to 5. So, simplifying the numerator results in the expression, \(\frac{5}{y(y + 5) * 5}\).
03

Simplify the Whole Expression

Simplify the whole expression by multiplying by the reciprocal of the denominator. In this case, the denominator to be considered is '5'. So, the final simplified expression is \(\frac{1}{y(y + 5)}\).

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Most popular questions from this chapter

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$

$$\text { Solve for } t: \quad s=-16 t^{2}+v_{0} t$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because I want to solve \(25 x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. You are choosing between two texting plans. Plan A has a monthly fee of \(\$ 15\) with a charge of \(\$ 0.08\) per text. Plan \(\mathbf{B}\) has a monthly fee of \(\$ 3\) with a charge of \(\$ 0.12\) per text. How many text messages in a month make plan A the better deal?

Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$
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