i need some help here.

[AlwaysAsking?s]

Hello math geniuses. I am jealous of your ability to figure this stuff out, but i am lost when it comes to solving rational equations. For example, I can not figure out this problem:
x-4=(6/x-4)
Here is what I am doing. Can you tell me what I am doing wrong, or how to solve it?
1. i found the lcm which is x-4 (is that correct?)
2. then i multiply both sides by x-4 and get: x^2 -4x-4x+16=6
3. i simplify that to: x^2-8x+16=6
4. then i subtract 6 to make it a quadratic equation and get: x^2-8x+10 but how do i factor that??

Thank you for your help, it really does mean alot, Im so frustrated and confused!

 

[tkhunny]

Oddly, your parentheses, which I am thrilled you decided to use, managed to create the wrong problem statement. You seem to have meant x - 4 = 6/(x-4)

lcm - What an odd thing. How much time did you spend finding hte LCM of one thing. "x-4" is all you have.

Domain Issues: You don't seem to have worried about x - 4 = 0. Since you don't know what 'x' might be, you must FIRST assure us all that your multiplication is not by the value zero (0). Watch. Is 4 = 5? Of course not. But, what if we multiply both sides by zero (0)? 4(0) = 0 and 5(0) = 0 and we get 0 = 0!! Wow!! No. Make sure what you use to multiply is NOT zero.

"subtract 6 to make it a quadratic equation" No. It was already a quadratic equation. Putting everything on one side and leaving zero on the other is no more quadratic than where we started. You probably mean some sort of standard form that you are used to seeing. Fair enough.

Factor? Why do you believe you should be able to factor it? You need to SOLVE it. Factoring is one way to go about that. The factorizations of 10 are very few. You have 1 * 10 and 2 * 5. That's it. You cannot get 8 out of either of those. 7 and 9 look like they have a chance, but 8 does not. What other tools have you for sloving such things? When you are done, if you get x = 4, something is wrong, since we already threw that out in the beginning.

 

[AlwaysAsking?s]

so the answer is no solution then since (x-4)(x-4)=6? I just do not understand that part. do we figure out what X will be to equal six?

but thank you so much for replying, i appreciate your help very much!

 

[Denis]

4. then i subtract 6 to make it a quadratic equation and get: x^2-8x+10 but how do i factor that??

That's correct...but really is x^2 - 8x + 10 = 0 ; an EQUATION ALWAYS has an = sign :shock:

Why are you confused? Just solve that equation for x using the quadratic formula;
that formula is there to rescue you in cases where you can't factor!

If you're not familiar with quadratic formula....hmmm: you SHOULD be! Go find out it's powers here:
http://en.wikipedia.org/wiki/Quadratic_equation

 

[tkhunny]

Why would you jump straight to "No Solution"? I recommend you try other methods besides factoring, first.