Rearranging Equations: Finding y in x = (y^3+1)/(y^2+1)

[Toby_Obie]

Homework Statement

Hello, I just need some quick help with the following, rearranging the below to make y the subject

Homework Equations

Rearrange x = (y^3+1)/(y^2+1) to find y

The Attempt at a Solution

Not sure , not been doing algebra for long

 

[tiny-tim]

Welcome to PF!

Hi Toby_Obie! Welcome to PF!

(try using the X² tag just above the Reply box )

Rearrange x = (y^3+1)/(y^2+1) to find y

Are you sure that's the question?

I don't think there's any way of making y the subject, without knowing the solution to a general cubic equation.

 

[Toby_Obie]

Question is correct - is it possible then ? There must be some way

 

[story645]

I don't think there's any way of making y the subject, without knowing the solution to a general cubic equation.

You're over complicating a bit. It's probably just solving the equation in terms of y, which itself just means moving somethings to the other side of the equals side.
Remember, what you do to one side of the equals sign, you do to the other side.

hints:
factor
get rid of fractions,
you'll have to move things around in both directions
the answer has a fraction

 

[Toby_Obie]

I'm searching for an answer in the following form :

y = f(x)

Can it be done

It may be over complicating but I have to know

Thanks for you help

 

[story645]

Can it be done

yes
factor y^3+1, simplify, and you should be able to work it out from there. It's just a lot of shuffling from one side of the equation to the other. Keep stuff in factored form and factor some more.

 

[Toby_Obie]

Sorry I don't get it

Could someone help me out ?

 

[tiny-tim]

sorry, not me … i don't get it either

 

[Toby_Obie]

I'm unsure how to release the x and y

x = (y^3+1)/(y^2+1)

x(y^2+1) = (y^3+1)

(xy^2)+x = y^3+1

x-1 = (y^3) - (xy^2) ?

Factoring (y^3+1) only creates (y+1)(y^2-y+1)

 

[story645]

sorry, not me … i don't get it either

I've spent way too many pages on this, but basically I think you just have to keep rearranging the equations (adding, subtracting, multiplying, dividing, multiplying) until everything simplifies.

Have you learned complex numbers yet? If so, you can use those to simplify things further.

 

[tiny-tim]

I've spent way too many pages on this, but basically I think you just have to keep rearranging the equations (adding, subtracting, multiplying, dividing, multiplying) until everything simplifies.

Have you learned complex numbers yet? If so, you can use those to simplify things further.

I repeat … I don't think there's any way of making y the subject, without knowing the solution to a general cubic equation.

 

[story645]

I repeat … I don't think there's any way of making y the subject, without knowing the solution to a general cubic equation.

Sorry, I was slow on the uptake and totally missing your hint.

 

[HallsofIvy]

I repeat … I don't think there's any way of making y the subject, without knowing the solution to a general cubic equation.

Sorry, I was slow on the uptake and totally missing your hint.

Hint? What hint? tiny-tim said exactly that in his first response and you said it was not true.

From $x= (y^3+ 1)/(y^2+ 1)$ we have $x(y^2+ 1)= xy^2+ x= y^3+ 1$ so $y^3- xy^2+ (1- x)= 0$. There no way to solve that for y, with general x, except by using the (very complicated!) cubic formula.

 

[Toby_Obie]

Thanks guys