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Explain one identity3(/x-1 -2/x+1 ):x+2/x^2-1=2

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uoor | Student, College Freshman | eNoter

Posted January 22, 2012 at 2:52 AM via web

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Explain one identity

3(/x-1 -2/x+1 ):x+2/x^2-1=2

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 22, 2012 at 3:00 AM (Answer #1)

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You need to establish the identity `(3/(x-1) -2/(x+1)):(x+2)/(x^2-1)=2. `

Notice that you need to multiply brackets by reverse of fraction `(x+2)/(x^2-1)`  such that:

`(3/(x-1) -2/(x+1))*(x^2 -1)/(x+2) = 2`

You need to bring the fractions in brackets to a common denominator such that:

`((3(x+1)-2(x-1))/(x-1)(x+1))*(x^2 -1)/(x+2) = 2`

Notice that you may write the common denominator as difference of squares such that:

`((3(x+1)-2(x-1))/(x^2 - 1))*(x^2 -1)/(x+2) = 2`

Reducing by (`x^2 - 1` ) yields:

`(3(x+1)-2(x-1))/(x+2) = 2`

You need to open the brackets to numerator such that:

`(3x + 3 - 2x + 2)/(x + 2) = 2`

`` `(x+5)/(x+2)=2 =gt x + 5 = 2x + 4`

The last line proves that the identity is not established.

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