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Which domain restrictions apply to the rational expression? add (-x-2/9x^2-1 )+ (-5x+4/9x^2-1) i meant for the numbers in

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Which domain restrictions apply to the rational expression? add (-x-2/9x^2-1 )+ (-5x+4/9x^2-1) i meant for the numbers in

Question

Which domain restrictions apply to the rational expression?
add
(-x-2/9x^2-1 )+ (-5x+4/9x^2-1)
i meant for the numbers in the parenthesis separated by / to be fractions

## Answers ( )

Both expression have the same denominator: 9x²-1. Thus it must not be 0.

9x²-1=(3x-1)(3x+1)=0, resulting x=+-1/3.

Restrictions: x in R\{-1/3, 1/3}

Adding those expressions:

E=(-x-2)/(9x²-1 ) + (-5x+4)/(9x²-1)=

(-x-2-5x+4)/(9x²-1)=(-6x+2)/(9x²-1)=

(-2)(3x-1)/(9x²-1)=-2/(3x+1)

E=-2/(3x+1)