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erma4kov [3.2K]
2 years ago
14

Simplify, state all restrictions.

Mathematics
1 answer:
Kipish [7]2 years ago
7 0

The simplified expression is \frac{1 - x - y}{x + y}and the restriction is y \ne -x

<h3>How to simplify the expression?</h3>

The expression is given as:

\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1

Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions

\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1

Rewrite the expression as products

\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1

Cancel out the common factors

\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1

Express 4x^2 - y^2 as (2x - y)(2x + y)

\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1

Cancel out the common factors

\frac{1}{x + y} -1

Take the LCM

\frac{1 - x - y}{x + y}

Hence, the simplified expression is \frac{1 - x - y}{x + y}and the restriction is y \ne -x

Read more about expressions at:

brainly.com/question/723406

#SPJ1

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