MHB Finding the Inverse of f(x) = x/(x+4)

[RidiculousName]

Hello, I am trying to find the inverse of f(x) = x $$ \div$$ (x+4)

IIRC i need to replace f(x) with y and solve for x.

I've tried to do y = x $$\div$$ (x+4) becomes y(x+4) = x then xy + 4y = x but I can't reduce the amount of x to one.

What am I doing wrong in this problem?

 

[I like Serena]

Hello, I am trying to find the inverse of f(x) = x $$ \div$$ (x+4)

IIRC i need to replace f(x) with y and solve for x.

I've tried to do y = x $$\div$$ (x+4) becomes y(x+4) = x then xy + 4y = x but I can't reduce the amount of x to one.

What am I doing wrong in this problem?

Hi Mr. Ridiculous, welcome to MHB! ;)

We can take it a couple of steps further:

xy + 4y = x
xy - x + 4y = 0
xy - x = -4y
x(y - 1) = -4y
x = -4y $$\div$$ (y-1)

 

[RidiculousName]

Thanks! I forgot I could leave the right side of the equation as zero.