Making x the subject of the equation (rational function).

Making x the subject of the equation (rational function). . 
These are two examples, one specific, and one more general, where you are given y as a function of x, and we want to find what x is in terms of y, so we want to make x the subject of the equation. Algebraic operations are used and details shown to solve this question. 

Question 1: If $y=\displaystyle{3x+1\over 7x-3}$, make $x$ the subject of the equation. 
Solution:

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and more generally, for all examples of this type we have 

Question 2: Suppose that $y=\displaystyle{ax+b\over cx+d}$, where $a,b,c,d$ are real numbers. Make $x$ the subject of the equation. (That is, find $x$ in terms of $y$ and $a,b,c,d$)
Solution