**CHECK MY WORK PWEASE?? **Am I doing this right? SOLVING INEQUALITY.

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**CHECK MY WORK PWEASE?? **Am I doing this right? SOLVING INEQUALITY.

Mathematics
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\[\frac{ 3 }{ x-1 }+\frac{ 2x}{ x+1 }>-1\]
\[\frac{ 3(x+1)+2x(x-1)+(x-1)(x+1) }{ (x-1)(x+1) } >0\]
\[\frac{ 3x^2+x-2 }{ (x-1)(x+1) }\]

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Other answers:

I did a sign chart but I get all positive, I know I must've done something wrong because the answer is \[(-\infty, -1) U (1,\infty)\]
I did a sign chart but I get all positive, I know I must've done something wrong because the answer is \[(-\infty, -1) U (1,\infty)\]
HI!!
there is some mistake here, lets see if we can find it
:)
first lets check the algebra
ok
ooh i see it!!
your numerator is wrong you wrote \[\frac{ 3x^2+x-2 }{ (x-1)(x+1) }\] but it should be \[\frac{ 3x^2+x+2 }{ (x-1)(x+1) }\]
Ohhhhhh I see it now too lol
now the numerator in this case is always positive so you can ignore it
and \[(x+1)(x-1)>0\] outside the zeros, on \(x<-1\) and \(x>1\)
So I only look at x=+1 then
zeros are at \(1\) and \(-1\)
Thank you! :D
I have another question, how do you find the domain of a function that has a fraction inside a square root? As in:\[f(x)=\sqrt{\frac{ x }{ x^2-2x-35 }}\]
I factored the denominator: (x-7)(x+5)
so x cannot equal 7 or -5

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