Question 306624
m over m-2 -3m over m-4 =-2m+2 over m squared -6m+8
:
Assume the problem is:
{{{m/((m-2))}}} - {{{(3m)/((m-4))}}} = {{{(-2m+2)/(m^2-6m+8)}}}
:
Factor the denominator on the right:
{{{m/((m-2))}}} - {{{(3m)/((m-4))}}} = {{{((-2m+2))/((m-4)(m-2))}}}
:
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