SOLUTION: i need help on solving for "m" in this rational expression m over m-2 -3m over m-4 =-2m+2 over m squared -6m+8

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Question 306624: i need help on solving for "m" in this rational expression
m over m-2 -3m over m-4 =-2m+2 over m squared -6m+8
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
m over m-2 -3m over m-4 =-2m+2 over m squared -6m+8
:
Assume the problem is:
m%2F%28%28m-2%29%29 - %283m%29%2F%28%28m-4%29%29 = %28-2m%2B2%29%2F%28m%5E2-6m%2B8%29
:
Factor the denominator on the right:
m%2F%28%28m-2%29%29 - %283m%29%2F%28%28m-4%29%29 = %28%28-2m%2B2%29%29%2F%28%28m-4%29%28m-2%29%29
:
Multiply by the common denominator,(m-4)(m-2), results:
m(m-4) - 3m(m-2) = -2m + 2
:
m^2 - 4m - 3m^2 + 6m = -2m + 2
Combine like terms on the left
m^2 - 3m^2 - 4m + 6m + 2m - 2 = 0
:
-2m^2 + 4m - 2 = 0
Factor out -2
-2(m^2 - 2m + 1) = 0
Factor again
-2(m-1)(m-1) = 0
Solution
m = 1