SOLUTION: 3x-5 over x-2 + 6x-13 over x-2 =9 3x=6x=9x 15=13=-18 9x-18 over x-2 ????

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Question 118467: 3x-5 over x-2 + 6x-13 over x-2 =9
3x=6x=9x
15=13=-18
9x-18 over x-2 ????
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28%283x-5%29%2F%28x-2%29%29%2B%28%286x-13%29%2F%28x-2%29%29=9

I'm not sure I understand what you were trying to say with the work you showed.

First thing is to realize that x = 2 makes the left side of the equation undefined, so if 2 comes up as a solution it needs to be excluded.

First, multiply both sides of the equation by x-2:

%283x-5%29%2B%286x-13%29=9%28x-2%29, then simplify:

9x-18=9x-18
9x=9x
x=x, which is true for all real x, except that we must exclude x = 2 because that makes the denominators in the original equation go to zero.

Hope that helps.
John

P.S. Ah! Now I get it. You were trying to say:

3x%2B6x=9x and
-5%2B%28-13%29=-18 and
you didn't understand how to divide %289x-18%29%2F%28x-2%29

Well, since 9x-18=9%28x-2%29, %289x-18%29%2F%28x-2%29=9, no matter what x is, so long as it isn't 2 because you can't divide by zero. Same result as above.

J.