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I need a little help with my homework.

This is the assingment: If: $$ U(x):= \frac{(x+2)^2}{x+1} $$ For what real numbers $x$ is defined: I tried to do that by solving the equation for $x$. I did that in following manner: $$ \frac{(x+2)^2}{x+1} = x+3+\frac{1}{x+1} $$ I got this solution by dividing $(x+2)^2$ with $x+1$. At the end I got that $x$ is $-1$ and $-3$.

Am I on a good track?? Thanks.

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It's defined for every $x\ne -1$ –  Riccardo.Alestra Oct 2 '13 at 16:11
    
Thanks. When I wrote question I figured that out. I fell a little bit stupid right now. –  depecheSoul Oct 2 '13 at 16:14

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up vote 3 down vote accepted

Your division is correct, but unnecessary.

What we know, however, is that $U(x)$ is defined for all $x\in \mathbb R, \;\;x \neq -1$. When $x = -1$, the denominator of $U(x)$ is zero, and division by zero is undefined.

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This also needs a TU! +1 –  Amzoti Oct 16 '13 at 0:39
    
A rain of $+$ for you. :-) –  Babak S. Oct 21 '13 at 6:59

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