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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q13. (page 731)

Simplify each expression.
$\frac{\frac{y^{2} + 10 y + 24}{y^{2} 鈭� 9}}{\frac{3 y^{2} + 17 y 鈭� 6}{2 y^{2} 鈭� 11 y + 15}}$

Short Answer

Expert verified

$\frac{(y + 4) (2 y 鈭� 5)}{(y + 3) (3 y 鈭� 1)}$

Step by step solution

01

Step 1. Division expression.

Write as a division expression.

$\frac{y^{2} + 10 y + 24}{y^{2} 鈭� 9} 梅 \frac{3 y^{2} + 17 y 鈭� 6}{2 y^{2} 鈭� 11 y + 15}$

02

Step 2. Divide.

To divide, multiply by the reciprocal.

$\frac{y^{2} + 10 y + 24}{y^{2} 鈭� 9} 鈰� \frac{2 y^{2} 鈭� 11 y + 15}{3 y^{2} + 17 y 鈭� 6}$

03

Step 3. Factor.

Factor the given expression and simplify.

$\frac{(y + 4) (y + 6)}{(y + 3) (y 鈭� 3)} 鈰� \frac{(2 y 鈭� 5) (y 鈭� 3)}{(y + 6) (3 y 鈭� 1)} = \frac{(y + 4) (2 y 鈭� 5)}{(y + 3) (3 y 鈭� 1)}$

Therefore, $\frac{\frac{y^{2} + 10 y + 24}{y^{2} 鈭� 9}}{\frac{3 y^{2} + 17 y 鈭� 6}{2 y^{2} 鈭� 11 y + 15}}$ can be simplified as $\frac{(y + 4) (2 y 鈭� 5)}{(y + 3) (3 y 鈭� 1)}$ .

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