Chapter 8: Q 224 (page 954)

Subtract $\frac{2 t - 30}{t^{2} + 6 t - 27} - \frac{2}{3 - t}$ .

Short Answer

Expert verified

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

Step by step solution

Given Information

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

Find the LCD of denominators.

$t^{2} + 6 t - 27 = (t - 3) (t + 9) (3 - t) = (- t + 3) L C D = (t - 3) (t + 9) (- t + 3)$

Rewrite the expression in factored form.

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

Rewrite each fraction as an equivalent fraction with the LCD.

$\to \frac{2 t - 30 (- t + 3)}{(t - 3) (t + 9) (- t + 3))} - \frac{- 2 (- t + 3) (t + 9)}{(t + 3) (t + 9) (- t + 3)}$

Subtract.

$\to \frac{(2 t - 30) (- t + 3) - (- 2 (- t + 3) (t + 9))}{(t + 3) (t + 9) (- t + 3)} \to \frac{(2 t - 30) (- t + 3) + 2 (- t + 3) (t + 9)}{(t + 3) (t + 9) (- t + 3)}$

Simplify and cancel common factors.

$\to \frac{- 4 t^{2} + 24 t - 36}{(t + 3) (t + 9) (- t + 3)} \to \frac{4}{t + 9}$

Thus, the result 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.

Subtract $\frac{2 t - 30}{t^{2} + 6 t - 27} - \frac{2}{3 - t}$ .

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Simplify and cancel common factors.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Geometry

Applied Mathematics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Subtract2t-30t2+6t-27-23-t.

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Simplify and cancel common factors.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Geometry

Applied Mathematics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Subtract $\frac{2 t - 30}{t^{2} + 6 t - 27} - \frac{2}{3 - t}$ .