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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. 8.19 (page 913)

Simplify: $\frac{y^{3} - 3 y^{2} + y - 3}{y^{2} - y - 6}$

Short Answer

Expert verified

The required answer is $\frac{y^{2} + 1}{y + 2}$

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{y^{3} - 3 y^{2} + y - 3}{y^{2} - y - 6}$

02

Step 2. Calculation

Factor the numerator and denominator using the grouping method and then remove the common factors.

$\frac{y^{3} - 3 y^{2} + y - 3}{y^{2} - y - 6} = \frac{y^{2} (y - 3) + 1 (y - 3)}{y^{2} - 3 y + 2 y - 6} = \frac{(y^{2} + 1) (y - 3)}{y (y - 3) + 2 (y - 3)} = \frac{(y^{2} + 1) (y - 3)}{(y + 2) (y - 3)} = \frac{y^{2} + 1}{y + 2}$

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