Maths linear graph help!!!!!

I received a question asking me to linearise y=3x/(1+x) ( put it in the form y= mx+c).
I was able to inverse the equation to get 1/y=(1+X)/3x , then by simply rearranging got 1/3x +x/3x. From here I'm a bit confused I know that the X in the x/3x should cancel to give 1/3. I need help for the final part.
Thanks in advance.

There's more than one way to linearise your equation.

Following your working, you have after cancellation:

$\displaystyle\frac{1}{y}= \frac{1}{3}\times \frac{1}{x}+ \frac{1}{3}$

And hopefully it's clear what X and Y are, and the equation of the line.

Hi thanks a lot for the help, should I now find the inverse of everything to get y=3/1× x/1 +3/1 to get the straight line equation y=3x+3