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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.5 (page 643)

Simplify $\frac{2 x^{2} - 12 x y + 18 y^{2}}{3 x^{2} - 27 y^{2}}$ .

Short Answer

Expert verified

The simplest form of the given expression is $\frac{2 (x - 3 y)}{3 (x + 3 y)} .$

Step by step solution

01

Step 1. Given information

The given expression is $\frac{2 x^{2} - 12 x y + 18 y^{2}}{3 x^{2} - 27 y^{2}} .$

02

Step 2. Simplify

$\frac{2 x^{2} - 12 x y + 18 y^{2}}{3 x^{2} - 27 y^{2}} = \frac{2 (x^{2} - 6 x y + 9 y^{2})}{3 (x^{2} - 9 y^{2})} Factorthenumeratoranddenominator = \frac{2 (x - 3 y) (x - 3 y)}{3 (x - 3 y) (x + 3 y)} = \frac{2 (x - 3 y)}{3 (x + 3 y)} Removethecommonfactorsofnumeratoranddenominator$

Hence, the simplified expression is $\frac{2 (x - 3 y)}{3 (x + 3 y)} .$

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