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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. 7.6 (page 643)

Simplify $\frac{5 x^{2} - 30 x y + 25 y^{2}}{2 x^{2} - 50 y^{2}} .$

Short Answer

Expert verified

The simplest form of the given expression

is $\frac{5 (x - y)}{2 (x + 5 y)} .$ $\frac{5 (x - y)}{2 (x + 5 y)} .$

Step by step solution

01

Step 1. Given information

The given information is $\frac{5 x^{2} - 30 x y + 25 y^{2}}{2 x^{2} - 50 y^{2}} .$

02

Step 2. Simplify

$\frac{5 x^{2} - 30 x y + 25 y^{2}}{2 x^{2} - 50 y^{2}} = \frac{5 (x^{2} - 6 x y + 5 y^{2})}{2 (x^{2} - 25 y^{2})} Factorizethenumeratoranddenominator = \frac{5 (x - y) (x - 5 y)}{2 (x + 5 y) (x - 5 y)} = \frac{5 (x - y)}{2 (x + 5 y)} Removethecommonfactorsofnumeratoranddenominator$

Hence, the simplified exression is $\frac{5 (x - y)}{2 (x + 5 y)} .$

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