Impossible algebra equation? I keep getting 'no solution'

[samsneaky]

is this right

7 | 7 | 11
------ = | ------ | + -----------------
x + 1 | x - 1 | X(squared) - 1

i keep coming up w/ -7 = 7 + 11
and anonther thing i keep coming up with is 7X = 7X + 14 + 11

I keep coming up with no solution i assume this is the correct answer ????

yes that is X(squared) i could not figure out how to type X squared on the keyboard.

Thank you that respond

 

[arthur ohlsten]

If the middle term is a absolute the equation has a answer.


if the equation is:
7/[x+1] = 7/[x-1] + 11/[x^2-1]
factor x^2-1

7/[x+1]=7/[x-1] + 11 / {[x-1][x+1]}
multiply both sides by [x-1][x+1] x not equal 1 or -1
7[x-1]=7[x+1]+11
7x-7=7x+7+11
0=25 impossible
There is no value of x that satisfys the original equation Answer!

I assume the equation did not have absolute terms
=================================================
If the original had a absolute term

7/[x+1] = 7/ l[x-1]l + 11/[x^2-1]

if this is true we have two equations

eq1) for x>1
7/[x+1] =7/[x+1] + 11/{x+1][x-1]
0=25 impossible no value of x satisfys this equation

eq2) for x<1
l x-1l = -x+1

7/[x+1]=7/[-x+1] + 11/{[x+1][x-1]}
7/[x+1]=-7/[x-1] + 11/{[x+1][x-1]
multiply by [x+1][x-1] for x not equal to 1 or -1
7[x-1] =-7[x+1] +11
7x-7 =-7x-7 +11
14x =11
x= 11/14 answer! this is less than 1

Arthur

 

[samsneaky]

arthur

thanks for your help but when you plug in your solution it does not work unless i am doing the math incorrectly please help

 

[o_O]

It does work if there is an absolute value expression. Is your equation:

\(\displaystyle \frac{7}{x+1} = \left|\frac{7}{x-1}\right| + \frac{11}{x^{2}-1}\)

or

\(\displaystyle \frac{7}{x+1} = \frac{7}{x-1} + \frac{11}{x^{2}-1}\) ?

If it's the first one, then it does work: you'll get 3.92 = 3.92
If it's the second one, then there is no solution as arthur, loren, and I have said (on both threads).

 

[arthur ohlsten]

7/[x+1] = 7/ l [x-1] l+ 11/{[x-1][x+1] let x= 11/14

[by the way absolute 7 = 7 ]

7/[25/14] = 7/l-3/14l + 11/{ -3/14][25/14]
l-3/14l=3/14
98/25 =98/3 -11[14][14]/75
multiply both sides by 75
294 =2450 -2156
294=294 Proof

Arthur