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Simplify the following: 1. (a^2 + 2ab + b^2)/(a + b) 2. (2x^2 + x - 6)/(2x + 4)

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anya4one | Student, Undergraduate | (Level 2) Honors

Posted August 15, 2011 at 3:53 AM via web

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Simplify the following:

1. (a^2 + 2ab + b^2)/(a + b)

2. (2x^2 + x - 6)/(2x + 4)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 15, 2011 at 4:11 AM (Answer #1)

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The two fractions to be simplified are:

1. (a^2 + 2ab + b^2)/(a + b)

use the relation (a + b)^2 = a^2 + 2ab + b^2

=> (a + b)^2/(a + b)

=> a + b

2. (2x^2 + x - 6)/ (2x + 4)

=> [2x^2 + 4x - 3x - 6]/(2x + 4)

=> [2x(x + 2) - 3(x + 2)]/(2*(x + 2))

=> (2x - 3)(x + 2)/2*(x + 2)

=> (2x - 3)/2

This gives (a^2 + 2ab + b^2)/(a + b) = (a + b) and (2x^2 + x - 6)/ (2x + 4) = (2x - 3)/2

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