Substitution to transform to quadratic form

**hexrei** · November 6th 2012, 04:58 PM

Can anyone help me with this?

$3=\frac{1}{(x+1)^2} + \frac{2}{(x+1)}$

I sub $u={(x+1)^-1}$

then flip them and rearrange so I get $u^2+\frac{u}{2}-3=0$

then mutiply all by two to get rid of fraction.

then I factor and end up with $(2u-3)(u+2)=0$

I think the problems begin when I sub back in the ${(x+1)^-1}$ ... doing something wrong and not getting book's solutions.

btw those -1's are supposed to be superscripted, not sure why its not working :/

**skeeter** · November 6th 2012, 05:09 PM

if $u = \frac{1}{x+1}$ , then the correct substitution would be ...

$3 = u^2 + 2u$

try again ...

**HallsofIvy** · November 6th 2012, 05:11 PM

$\frac{1}{a}+ \frac{1}{b}$ "flipped" does NOT give "a+ b".

**hexrei** · November 6th 2012, 05:17 PM

Originally Posted by skeeter

if $u = \frac{1}{x+1}$ , then the correct substitution would be ...

$3 = u^2 + 2u$

try again ...

I appreciate the help

and of course I'm going to try again. Why would I have taken the time to post it otherwise

**hexrei** · November 6th 2012, 06:11 PM

OK, so I have wrapped my head around that early error I made.

I'm getting tripped up after the factorization still though, and the book unfortunately has example subbing with negative exponents with single variable but none with a constant and a variable plus negative exponent.

So after I sub $x+1^{-1}$ back in. I will only list one of the zeros since I think once I see what I am missing the second shouldn't be hard.

my factorization is now $(u+3)(u-1)=0$

which after subbing back in the first one yields me

$\frac{1}{x+1} + 3$

from there I tried finding a common denominator

$\frac{1}{x+1} + \frac{3x+3}{x+1}$

and adding them like so

$\frac{3x+4}{x+1}$

But not sure if that was correct, or what to do next. Can someone give me a clue please?

**MarkFL** · November 6th 2012, 06:24 PM

When is a rational expression equal to zero?

**hexrei** · November 6th 2012, 06:27 PM

Originally Posted by MarkFL2

When is a rational expression equal to zero?

oooh..... when the numerator is zero? So x would be -4/3. Got it. Thanks

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