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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. 213 (page 694)

In the following exercises, solve each rational equation.
$\frac{v - 10}{v^{2} - 5 v + 4} = \frac{3}{v - 1} - \frac{6}{v - 4}$

Short Answer

Expert verified

There is no solution.

Step by step solution

01

Step 1. Given

The given equation is: $\frac{v - 10}{v^{2} - 5 v + 4} = \frac{3}{v - 1} - \frac{6}{v - 4}$

02

Step 2. To find

We have to solve the equation.

03

Step 3. Calculation

The denominators are never 0. So, $v 鈮� 1, 4$ .

We multiply both sides by the LCD, then solve the linear equation.

$\frac{v - 10}{v^{2} - 5 v + 4} = \frac{3}{v - 1} - \frac{6}{v - 4} \frac{v - 10}{(v - 1) (v - 4)} = \frac{3}{v - 1} - \frac{6}{v - 4} \frac{v - 10}{(v - 1) (v - 4)} (v - 1) (v - 4) = \frac{3}{v - 1} (v - 1) (v - 4) - \frac{6}{v - 4} (v - 1) (v - 4) v - 10 = 3 (v - 4) - 6 (v - 1) v - 10 = 3 v - 12 - 6 v + 6 v - 10 = - 3 v - 6 v + 3 v = 10 - 6 4 v = 4 v = 1$

But $v 鈮� 1$ . Hence, there is no solution.

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Most popular questions from this chapter

Solve the proportion $\frac{z}{z - 84} = - \frac{1}{5}$ .

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

$\frac{1}{2} - \frac{3}{2 x^{2}} 鈮� \frac{1}{x}$

In the following exercise, perform the indicated operation:

$\frac{3}{2 x^{2} + 5 x + 2} - \frac{1}{2 x^{2} + 3 x + 1}$

Write the steps to find the solution to the given equation.

In the following exercises, find the domain of each function.

$R (x) = \frac{x^{3} + 3 x^{2} - 4 x - 12}{x^{2} - 4}$

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