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Simplifying Rational Expressions Simplify, leaving each answer in factored form.

Simplifying Rational Expressions Simplify, leaving each answer in factored form.-example-1
User Davidallyoung
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Third question

The given expression is

(2x^2 + xy - y^2)/(3x^2 + 3xy)

The numerator can be written in factored form. Thus,

2x^2 + xy - y^2 = (2x - y)(x + y)

The expression becomes

(2x - y)(x + y)/(3x^2 + 3xy)

Looking at the denominator, 3x is common to both terms. If we factor out 3x in the denominator, it becomes 3x(x + y). The expression becomes

(2x - y)(x + y)/3x(x + y)

x + y is common to both the numerator and denominator. Thus, they can cancel out. The simplified expression would be

(2x - y)/3x

User Iamdlm
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