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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 113. (page 931)

Divide Rational Expressions: $\frac{t^{2} 鈥� 鈭� 鈥� 9}{2 t} 梅 (t^{2} 鈥� 鈭� 鈥� 6 t 鈥� + 鈥� 9)$

Short Answer

Expert verified

The required answer is $\frac{t + 3}{2 t (t - 3)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $\frac{t^{2} 鈥� 鈭� 鈥� 9}{2 t} 梅 (t^{2} 鈥� 鈭� 鈥� 6 t 鈥� + 鈥� 9)$ .

02

Step 2. Simplify the expression.

$\frac{t^{2} 鈥� 鈭� 鈥� 9}{2 t} 梅 (t^{2} 鈥� 鈭� 鈥� 6 t 鈥� + 鈥� 9) = \frac{\frac{t^{2} - 9}{2 t}}{t^{2} - 6 t + 9}$

Apply the fraction rule.

$\frac{t^{2} - 9}{2 t (t^{2} - 6 t + 9)} = \frac{(t + 3) (t - 3)}{2 t (t^{2} - 6 t + 9)} = \frac{(t + 3) (t - 3)}{2 t {(t - 3)}^{2}}$

03

Apply exponent law.

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

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Most popular questions from this chapter

Efraim wants to start simplifying the complex fraction $\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a} - \frac{1}{b}}$ by cancelling the variables from the numerator and denominator. Explain what is wrong with Efraim鈥檚 plan.

Solve Proportions

$\frac{d}{d 鈭� 48} = 鈭� \frac{13}{3}$

Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child鈥檚 weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 pounds?

In the following exercises, solve.

$\frac{x - 10}{x^{2} + 8 x + 12} = \frac{3}{x + 2} + \frac{4}{x + 6}$

Simplify

In the following exercises, use either method.

$\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}}$ .

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