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

  • Thread starter JKaufinger
  • Start date
In summary, to solve for x in the equation y = (x+4)/(x+3), you can first multiply both sides by (x+3) to eliminate the fraction. This gives you xy + 3y = x + 4. Then, you can rearrange the terms to get x-xy = 3y-4. Finally, you can factor out x and solve for it by dividing both sides by (1-y), giving you x = (3y-4)/(1-y).
  • #1
JKaufinger
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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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  • #2
Well you can continue as follows:
x-xy=3y-4
x=(3y-4)/(1-y)
 
  • #3
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
 

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

Can the equation y = (x+4)/(x+3) be solved for x?

Yes, the equation can be solved for x.

What is the process for solving this equation for x?

To solve for x in this equation, you must first isolate the variable x on one side of the equation. This can be done by multiplying both sides by (x+3) to eliminate the denominator. Then, you can simplify the equation and solve for x using basic algebraic techniques.

Are there any restrictions for the values of x in this equation?

Yes, there are restrictions for the values of x in this equation. The denominator (x+3) cannot equal 0, so x cannot be equal to -3. This is because dividing by 0 is undefined in mathematics.

Can this equation have more than one solution for x?

Yes, it is possible for this equation to have more than one solution for x. This will depend on the specific values of y and the restrictions mentioned in the previous question.

Is there a specific method or formula for solving this type of equation?

Yes, this type of equation is a rational equation, which can be solved using a specific method or formula. However, the exact method or formula used may vary depending on the specific structure of the equation. In general, isolating the variable and simplifying the equation is a common approach for solving rational equations.

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