Q. 226 In the following exercises, solv... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 226 (page 694)

In the following exercises, solve each rational equation.
$\frac{t}{6 t - 12} - \frac{5}{2 t + 10} = \frac{t^{2} - 23 t + 70}{12 t^{2} + 36 t - 120}$ .

Short Answer

Expert verified

There is no solution.

Step by step solution

Step 1. Given

The given equation is: $\frac{t}{6 t - 12} - \frac{5}{2 t + 10} = \frac{t^{2} - 23 t + 70}{12 t^{2} + 36 t - 120}$ .

Step 2. To find

We have to solve the equation.

Step 3. Calculation

Factor the denominators.

$\frac{t}{6 t - 12} - \frac{5}{2 t + 10} = \frac{t^{2} - 23 t + 70}{12 t^{2} + 36 t - 120} \frac{t}{6 (t - 2)} - \frac{5}{2 (t + 5)} = \frac{t^{2} - 23 t + 70}{12 (t^{2} + 3 t - 10)} \frac{t}{6 (t - 2)} - \frac{5}{2 (t + 5)} = \frac{t^{2} - 23 t + 70}{12 (t - 2) (t + 5)}$

The denominator is never 0. So, $t 鈮� 2, - 5$

We multiply both sides by LCD and then solve the equation.

$\frac{t}{6 (t - 2)} - \frac{5}{2 (t + 5)} = \frac{t^{2} - 23 t + 70}{12 (t - 2) (t + 5)} \frac{t}{6 (t - 2)} 12 (t - 2) (t + 5) - \frac{5}{2 (t + 5)} 12 (t - 2) (t + 5) = \frac{t^{2} - 23 t + 70}{12 (t - 2) (t + 5)} 12 (t - 2) (t + 5) 2 t (t + 5) - 30 (t - 2) = t^{2} - 23 t + 70 2 t^{2} + 10 t - 30 t + 60 = t^{2} - 23 t + 70 2 t^{2} - 20 t + 60 = t^{2} - 23 t + 70 t^{2} + 3 t - 10 = 0 (t + 5) (t - 2) = 0 t = - 5, 2$

But $t 鈮� - 5, 2$ . So there is no solution.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercises, solve each rational equation.
$\frac{t}{6 t - 12} - \frac{5}{2 t + 10} = \frac{t^{2} - 23 t + 70}{12 t^{2} + 36 t - 120}$ .

Short Answer

Step by step solution

Step 1. Given

Step 2. To find

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

91影视

In the following exercises, solve each rational equation.t6t-12-52t+10=t2-23t+7012t2+36t-120.

Short Answer

Step by step solution

Step 1. Given

Step 2. To find

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each rational equation.
$\frac{t}{6 t - 12} - \frac{5}{2 t + 10} = \frac{t^{2} - 23 t + 70}{12 t^{2} + 36 t - 120}$ .