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Mathematics
OpenStudy (anonymous):

\[\left( 1 \over x +1 \right)-2\left( 1\over x+1 \right)-8=0\]

OpenStudy (amistre64):

if we multiply it all by (x+1) we can clear out the fractional parts

OpenStudy (amistre64):

1-2-8(x+1) = 0

OpenStudy (amistre64):

1 -2 -8x -8 = 0 -9 -8x = 0 -8x = 9 x = -9/8 maybe?

OpenStudy (amistre64):

:) that does make a difference; and please refrain from typing in profanity. We want to keep the place clean.

OpenStudy (amistre64):

substitute [1/(x+1)] with a different variable like; b then it becomes b^2 -2b -8 = 0, and we can solve for b

OpenStudy (amistre64):

(b-4) (b+2) ; b= 4 and -2 since b= 1/(x+1) this means \[\frac{1}{x+1}=4 \ or -2\]

OpenStudy (anonymous):

ah i see. answer is: -3/2 and -3/4

OpenStudy (amistre64):

\[\frac{1}{x+1}=4\iff 1 = 4x +4\] \[4x = -3 \iff x = -3/4\] also \[\frac{1}{x+1}=-2\iff 1= -2x-2\] \[3 = -2x \iff x = -3/2\] yes, very good :)

OpenStudy (anonymous):

why can't we take \[\left( 1 \over x + 1 \right)^2\] and write it as: \[\left( 1 \over x+1 \right)\left( 1 \over x+1 \right)\]?

OpenStudy (amistre64):

we can, but it really doesnt lead to an easier solution to the problem.

OpenStudy (anonymous):

it's just the way that i learned and was wondering if i was doing it a way that was wrong... thanks for clearing it up on that :)

OpenStudy (amistre64):

youre welcome :)

OpenStudy (anonymous):

or... how am i doing it wrong?

OpenStudy (amistre64):

since that is neither equal to -3/2 or -3/4 ..... I would have to see how you are trying to solve it.

OpenStudy (amistre64):

n^2 -2n -8 = 0 ; are you attempting to factor the first 2? n(n-2) -8 = 0 n(n-2) = 8 ??

OpenStudy (anonymous):

i wrote it as: \[\left( 1 \over x+1 \right)\left( 1 \over x+1 \right)\] then used common denominator. it leaves me with 1*1 which doesn't seem right...

OpenStudy (amistre64):

the common denom for all of them would then be what: x^2 +2x +1 right?

OpenStudy (anonymous):

that would become the new denominator from 1/(x+1) times 1/(x+1)?

OpenStudy (amistre64):

\[\frac{1}{x^2+2x+ 1}-\frac{2(x+1)}{x^2+2x+1}-\frac{8(x^2+2x+1)}{x^2+2x+1}\]

OpenStudy (amistre64):

which then amounts to just focusing on the top since that is what makes a fraction = 0 \[1-2x-2-8x^2-16x-8\]

OpenStudy (anonymous):

hmmm... i'm trying to understand. you have been really helpful. i am going to work through this problem a time or two more...

OpenStudy (amistre64):

good luck with it :)

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