SOLUTION: Can you help me solve this equation? {{{2/(x-3)+2/x=1}}}

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Question 548292: Can you help me solve this equation?
2%2F%28x-3%29%2B2%2Fx=1
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28x-3%29%2B2%2Fx=1
I don't know about you... but I do not like having fractions... lets get rid of them!
To do this, we will first multiply every term by x-3 to get
%28x-3%29%2A%282%2F%28x-3%29%29%2B%28x-3%29%2A%282%2Fx%29=%28x-3%29%2A1
2%2B%282x-6%2Fx%29=%28x-3%29
Now let's multiply every term by x
x%2A2%2Bx%2A%282x-6%2Fx%29=x%2A%28x-3%29
2x%2B2x-6=x%5E2-3x
4x-6=x%5E2-3x
This is just a quadratic, so lets put it in the form ax^2+bx+c=0
4x-6-4x%2B6=x%5E2-3x-4x%2B6
0=x%5E2-7x%2B6
Now we need to think of two numbers that multiply to our c value (6) and add to our b value (-7) ... if you think hard enough you will find that -1 and -6 does the trick.
So our equation factors to
%28x-1%29%28x-6%29=0
Now if two things have a product of 0, then at least one of them must be equal to 0
This means
x-1=0
x=1
or
x-6=0
x=6

And there is the two solutions:)