Solving for x in y = (x+4)/(x+3): Is it Possible?

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To solve for x in the equation y = (x+4)/(x+3), one can start by cross-multiplying to eliminate the fraction, resulting in y(x+3) = (x+4). Rearranging the equation leads to a form where x can be isolated, ultimately yielding x = (3y-4)/(1-y). This method demonstrates that solving for x in such equations is indeed possible, despite initial confusion with the variable's placement in both the numerator and denominator. The process highlights the importance of algebraic manipulation in solving rational equations.
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Homework Statement


How would you solve for x in y = (x+4)/(x+3)


Homework Equations





The Attempt at a Solution


y(x+3) = (x+4)
xy+3y=x+4
-x+xy+3y=4
x-xy-3y=-4

... That is the closest to anything familiar I could come.

This isn't really a homework question but how would you do this? Is it even possible?
 
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Well you can continue as follows:
x-xy=3y-4
x=(3y-4)/(1-y)
 
Wow... I can't believe that it was a simple 2 steps from there. I just seem to have a problem with solving for x when it is in a numerator and denominator (I had another problem like this and someone else had to figure it out for me)

lol

thanks
 

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