help please
solve the following equation for x
x+1/x+6 = x-1/x+3
the solution is x = ---?

Question

radar · Answer

(x-1)(x+6)=x^2+5x-6)

anonymous · Answer

$$\frac{x+1}{x+6}=\frac{x-1}{x+3}$$
The easiest thing to do would be to get rid of the fractions.  We are going to do this by multiplying both sides by the denominators.  We have to notice that, when we do this, we might be introducing another incorrect solution (this might happen whenever you multiply by x).  We will need to check the solution at the end.

First, multiply both sides by x+6.  On the left side, the division by x+6 will cancel with the division, and we will be left with x+1
$$x+1=\frac{(x-1)(x+6)}{x+3}$$
Next, we want to get rid of the x+3 in the denominator.  Multiply by x+3 to get rid of it, and then multiply the other side by x+3 to keep the equation in balance.
$$(x+1)(x+3)=(x-1)(x+6)$$
FOIL (Expand)
$$x^2+4x+3=x^2+5x-6$$
Subtract x^2 from both sides.
$$4x+3=5x-6$$
Subtract 4x from both sides to get all the x terms on one side.
$$3=x-6$$
Add 6 to both sides to get x by itself.  
$$x=9$$
Check by substituting 9 back into the original equation.  

In the solution submitted above, 4 does not work when substituted back into the original equation.  The solution should be x = 9.

anonymous · Answer

My mistake!

anonymous · Answer

Sorry, I wasn't trying to dog on you or anything like that!

anonymous · Answer

Oh no! That's what happens when you aren't paying attention! :)