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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.67 (page 685)

Solve: $1 - \frac{2}{x} = \frac{15}{x^{2}}$ .

Short Answer

Expert verified

The solution is $x = 5, - 3$ .

Step by step solution

01

Step 1. Given.

The given equation is: $1 - \frac{2}{x} = \frac{15}{x^{2}}$ .

02

Step 2. To find

We have to solve the given equation.

03

Step 3. Calculation

The LCD is $x^{2}$ . Multiply both sides of the equation by LCD. Then we solve the linear equation.

$1 - \frac{2}{x} = \frac{15}{x^{2}} 1 (x^{2}) - \frac{2}{x} (x^{2}) = \frac{15}{x^{2}} (x^{2}) x^{2} - 2 x = 15 x^{2} - 2 x - 15 = 0 (x - 5) (x + 3) = 0 x = 5, - 3$

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Most popular questions from this chapter

Xander’s new business found that the daily demand for its product was inversely proportional to the price $p$ . When the price is \(5, the demand is 700 units.

Write the equation of variation.
What is the demand if the price is raised to $\) 7$ ?

Solve the rational equation $\frac{E}{c} = m^{2}$ for the variable c.

Determine the values for which the rational expression is undefined.

$\frac{x - 3}{x^{2} - x - 30}$

In the following exercise, find

(a) $R (x) = f (x) + g (x)$

(b) $R (x) = f (x) - g (x)$ :

$f (x) = \frac{6 x}{x^{2} - 64} g (x) = \frac{3}{x - 8}$

Simplify $\frac{9 m^{4}}{18 {mn}^{3}}$

See all solutions

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