# Algebra problem.... me again

• Aug 24th 2007, 02:25 PM
JonathanEyoon
Algebra problem.... me again
The problem is

2 + (1 / y + 1) - (1 / y - 1) = 0

Ok what I did was Mulitply the entire equation by the common denominator of

(y + 1)(y - 1).

I end up getting

2(y + 1)(y - 1) + y - 1 - y + 1 = 0

From here, I keep working the problem until it gets to

2(y^2 - 1) = 0

2y^2 - 2 = 0

(2y^2 - 2) / 2

y^2 - 1 = 0

y^2 = 1

Square root both sides to get

y = +- 1

The problem is, when entering either one of these solutions into the original problem, i'm always getting one of the divisions within the problem where the denominator is 0 and that is undefined....so i'm kinda lost. Is there no solution or?
• Aug 24th 2007, 02:28 PM
Jhevon
Quote:

Originally Posted by JonathanEyoon
2(y + 1)(y - 1) + y - 1 - y + 1 = 0

you made a mistake in this line:

it is, 2(y + 1)(y - 1) + (y - 1) - (y + 1) = 0

=> 2(y + 1)(y - 1) + y - 1 - y - 1 = 0
• Aug 24th 2007, 02:32 PM
JonathanEyoon
Quote:

Originally Posted by Jhevon
you made a mistake in this line:

it is, 2(y + 1)(y - 1) + (y - 1) - (y + 1) = 0

=> 2(y + 1)(y - 1) + y - 1 - y - 1 = 0

DOH!!! thanks for pointing that out

So the end solution should instead be

Y = +- Squareroot of 2
• Aug 24th 2007, 02:34 PM
Jhevon
Quote:

Originally Posted by JonathanEyoon
DOH!!! thanks for pointing that out

So the end solution should instead be

Y = +- Squareroot of 2

yes :)
• Aug 24th 2007, 02:38 PM
JonathanEyoon
Quote:

Originally Posted by Jhevon
yes :)

MmMm.... how would I punch that into a Ti-83 calculator to double check? I'm putting it into the calculator like this

2 + (1 / (squareroot 2) + 1) - (1 / (squareroot 2) - 1

The answer comes out to 4 instead of 0 for both postive and negative squareroot of 2. :(
• Aug 24th 2007, 02:41 PM
Jhevon
Quote:

Originally Posted by JonathanEyoon
MmMm.... how would I punch that into a Ti-83 calculator to double check? I'm putting it into the calculator like this

2 + (1 / (squareroot 2) + 1) - (1 / (squareroot 2) - 1

The answer comes out to 4 instead of 0 for both postive and negative squareroot of 2. :(

you forgot the last bracket. it should be:

2 + (1 / ((squareroot 2) + 1)) - (1 / ((squareroot 2) - 1))

i punched it into my regular scientific calculator and got 0
• Aug 24th 2007, 02:46 PM
JonathanEyoon
Quote:

Originally Posted by Jhevon
you forgot the last bracket. it should be:

2 + (1 / ((squareroot 2) + 1)) - (1 / ((squareroot 2) - 1))

i punched it into my regular scientific calculator and got 0

:) You are awesome!