Can You Simplify and Solve This Complex Equation for y?

[CourtneyS]

Homework Statement

I am supposed to solve this equation for y.

Homework Equations

0=-(x+0.91)/(y^2+(x+0.91)^2 )+ (x-0.91)/(y^2+(x-0.91)^2)

The Attempt at a Solution

I moved one of the terms to the other side and saw no way to get the solution doing that so then I got a CD by doing this:

[ (x+.91)(y^2 + (x-0.91)^2) - (x-0.91)(y^2+(x+0.91)^2) ] / [ (y^2 + (x+0.91)^2) (y^2 + (x-0.91)^2 ]

Then expanded

{xy^2 + x(x+0.91)^2 - 0.91y^2 + 0.91(x+0.91)^2 - [xy^2 +x(x+0.91)^2 - 0.91y^2 - 0.91(x+0.91)^2]} / [y^22 + y^2(x+0.91)^2 + y^2(x-0.91)^2 + (x+0.91)^2*(x-0.91)^2]

I don't really think expanding helps at all but I didn't know what else to so cause I didn't see a solution from the earlier eqn.

Any suggestions?[/B]

 

[LCKurtz]

Homework Statement

I am supposed to solve this equation for y.

Homework Equations

0=-(x+0.91)/(y^2+(x+0.91)^2 )+ (x-0.91)/(y^2+(x-0.91)^2)

The Attempt at a Solution

I moved one of the terms to the other side and saw no way to get the solution doing that so then I got a CD by doing this:

[ (x+.91)(y^2 + (x-0.91)^2) - (x-0.91)(y^2+(x+0.91)^2) ] / [ (y^2 + (x+0.91)^2) (y^2 + (x-0.91)^2 ]

Then expanded

{xy^2 + x(x+0.91)^2 - 0.91y^2 + 0.91(x+0.91)^2 - [xy^2 +x(x+0.91)^2 - 0.91y^2 - 0.91(x+0.91)^2]} / [y^22 + y^2(x+0.91)^2 + y^2(x-0.91)^2 + (x+0.91)^2*(x-0.91)^2]

I don't really think expanding helps at all but I didn't know what else to so cause I didn't see a solution from the earlier eqn.

Any suggestions?[/B]

Yes. First suggestion is call $a=.91$. Second is to use tex and write it as$$
\frac{x+a}{y^2+(x+a)^2}=\frac {x-a}{y^2+(x-a)^2}$$Now invert both sides and you should be able to solve it for $y^2$.