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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q.493. (page 742)

Solve the equation.
$\frac{1}{z - 5} + \frac{1}{z + 5} = \frac{1}{z^{2} - 25}$

Short Answer

Expert verified

The solution is $z = \frac{1}{2}$ .

Step by step solution

01

Step 1. Given information.

The given equation is $\frac{1}{z - 5} + \frac{1}{z + 5} = \frac{1}{z^{2} - 25}$ .

02

Step 2. Simplify the equation.

$\begin{array}{rcl} \frac{1}{z - 5} + \frac{1}{z + 5} & = & \frac{1}{z^{2} - 25} \\ \frac{z + 5 + z - 5}{(z^{2} - 25)} & = & \frac{1}{z^{2} - 25} \\ \frac{2 z}{(z^{2} - 25)} 脳 (z^{2} - 25) & = & \frac{1}{(z^{2} - 25)} 脳 (z^{2} - 25) \\ 2 z & = & 1 \\ z & = & \frac{1}{2} \end{array}$

03

Step 3. Simplified answer.

Hence, the required solution is $z = \frac{1}{2}$ .

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Most popular questions from this chapter

If y varies directly as x and $y = 14$ , when $x = 3$ . Find the equation that relates x and y.

In the following exercises, divide the rational expressions.

$\frac{v - 5}{11 - v} 梅 \frac{v^{2} - 25}{v - 11}$

Solve the proportion $\frac{y}{y + 55} = \frac{3}{8}$ .

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{4}{x^{2} - 25} > 0$

Solve each rational function inequality and write the solution in interval notation. Given the function $R (x) = \frac{(x + 1)}{(x - 4)},$ find the values of x that make the function less than or equal to 0.

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