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Simplify: `x/ (x^2 + 2x + 1) + 1/(x^2 + 5x + 4)` Leave answer in factored form....

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted September 15, 2013 at 5:32 AM via web

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Simplify:

`x/ (x^2 + 2x + 1) + 1/(x^2 + 5x + 4)`

Leave answer in factored form.  Include parenthesis around polynomials in the numerator and/or denominator.

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted September 15, 2013 at 5:57 AM (Answer #1)

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`x/(x^2+2x+1)+1/(x^2+5x+4)=`

Now we factor both denominators.

`x/(x+1)^2+1/((x+1)(x+4))=`

Common denominator is `(x+1)^2(x+4)`

`(x(x+4)+x+1)/((x+1)^2(x+4))=(x^2+5x+1)/((x+1)^2(x+4))`   <-- Your solution

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