SOLUTION: Hopefully someone can help me with this one. Thanks! x / x-2 = 2/x-3 we are solving for x. Thanks!

Algebra ->  Expressions-with-variables -> SOLUTION: Hopefully someone can help me with this one. Thanks! x / x-2 = 2/x-3 we are solving for x. Thanks!      Log On


   

Question 60985: Hopefully someone can help me with this one. Thanks!
x / x-2 = 2/x-3 we are solving for x.
Thanks!
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x-2%29+=+2%2F%28x-3%29
Multiple both sides by x-3
Then x%28x-3%29%2F%28x-2%29+=+2
Now multiply both sides by x-2
Then x%28x-3%29+=+2%28x-2%29
Multiply both sides out.
Then x%5E2-3x+=+2x-4
Subtract 2x from both sides.
Then x%5E2-5x+=+-4
Now add 4 to both sides.
Then x%5E2-5x%2B4+=+0
This is a quadratic equation which factors:
%28x-1%29%28x-4%29+=+0
So, x=1 and x=4 are the two solutions.
To verify, plug 1 and 4 into the original equation x%2F%28x-2%29+=+2%2F%28x-3%29
1%2F%281-2%29+=+-1 which is indeed equal to 2%2F%28-2%29
And, 4%2F%284-2%29+=+4%2F2+=+2 which is indeed equal to 2%2F%284-3%29 which = 2