Finding the Domain and Solving an Equation with Rational Functions

[Quisquis]

1. The problem, as stated:

What is the largest set of real numbers on which the function whose rule is $$f(x)=\frac{3x+4}{2x+9}$$ can be defined? Solve the equation $$y=f(x)$$ for x.

2. The attempt at a solution

I've done the first part of the equation after realizing that "...the largest set of real numbers..." just meant the domain, but I've really got no idea what to do with the last part.

I've tried multiplying the top and bottom by the denominator... multiplying both sides to clear out the denominator. A bunch of different stuff that doesn't seem to get me anywhere.

I would really appreciate it if I could get some help as to where to go with this.

-Quisquis

 

[snipez90]

After clearing denominators, try to move the terms with an x to one side and the other terms to the other side. Then factor out an x and divide.

 

[Quisquis]

After like 20 more minutes of messing with it after your advice, I figured it out.

Thanks a lot.