Q. 121 In the following exercises, perf... [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. 121 (page 668)

In the following exercises, perform indicated operations.
$\frac{t}{t - 6} - \frac{t - 2}{t + 6}$

Short Answer

Expert verified

The resultant expression is $\begin{array}{rcl} \frac{2 (7 t - 6)}{(t - 6) (t + 6)} \end{array}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{t}{t - 6} - \frac{t - 2}{t + 6}$ .

Step 2. Express with common denominator

The LCD of the terms of obtained expression is $(t - 6) (t + 6)$ .
Multiply the numerator and denominator of first term by $(t + 6)$ and second term by $(t - 6)$ .

role="math" localid="1645432004980" $\begin{array}{rcl} \frac{t (t + 6)}{(t - 6) (t + 6)} - \frac{(t - 2) (t - 6)}{(t + 6) (t - 6)} & = & \frac{t^{2} + 6 t}{(t - 6) (t + 6)} - \frac{t^{2} - 2 t - 6 t + 12}{(t + 6) (t - 6)} \\ = & \frac{t^{2} + 6 t}{(t - 6) (t + 6)} - \frac{t^{2} - 8 t + 12}{(t + 6) (t - 6)} \end{array}$

Step 3. Simplify

As the denominator is the same for both the terms, perform subtraction in the numerator and place it over the common denominator.

$\begin{array}{rcl} \frac{t^{2} + 6 t - t^{2} + 8 t - 12}{(t - 6) (t + 6)} \end{array} = \begin{array}{rcl} \frac{14 t - 12}{(t - 6) (t + 6)} \end{array}$

Factor the numerator and express it in the lowest terms possible.

$\begin{array}{rcl} \frac{2 (7 t - 6)}{(t - 6) (t + 6)} \end{array}$

So, the resultant expression is $\begin{array}{rcl} \frac{2 (7 t - 6)}{(t - 6) (t + 6)} \end{array}$ .

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, perform indicated operations.
$\frac{t}{t - 6} - \frac{t - 2}{t + 6}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

91影视

In the following exercises, perform indicated operations. tt-6-t-2t+6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{t}{t - 6} - \frac{t - 2}{t + 6}$