Chapter 7: Q. 130 (page 668)

In the following exercises, perform indicated operations.
$\frac{2 t - 30}{t^{2} + 6 t - 27} - \frac{2}{3 - t}$

Short Answer

Expert verified

The resultant expression is $\frac{4}{t + 9}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{2 t - 30}{t^{2} + 6 t - 27} - \frac{2}{3 - t}$ .

Step 2. Express with LCD

The LCD of the given terms is $(t + 9) (t - 3)$ .
Express the given expression with the LCD.

localid="1646140499486" $\frac{2 t - 30}{t^{2} + 6 t - 27} - \frac{2}{3 - t} = \frac{2 t - 30}{(t + 9) (t - 3)} - \frac{- 2 t + 18}{(t + 9) (t - 3)}$

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.

$\frac{2 t - 30 + 2 t - 18}{(t + 9) (t - 3)} = \frac{4 t - 12}{(t + 9) (t - 3)}$

Factor the numerator and cancel out the common factor from numerator and denominator.

$\frac{4 (t - 3)}{(t + 9) (t - 3)} = \frac{4}{t + 9}$

So, the resultant expression is $\frac{4}{t + 9}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, perform indicated operations.
$\frac{2 t - 30}{t^{2} + 6 t - 27} - \frac{2}{3 - t}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with LCD

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Probability and Statistics

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.2t-30t2+6t-27-23-t

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with LCD

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Probability and Statistics

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{2 t - 30}{t^{2} + 6 t - 27} - \frac{2}{3 - t}$