Question 151208
{{{(x-3)/(4-2x) - 1/(x-2) + 1 = 0}}} Start with the given equation.



{{{(x-3)/(-2(x-2)) - 1/(x-2) + 1 = 0}}} Factor {{{4-2x}}} to get {{{4-2x=2(2-x)=-2(x-2)}}}



{{{(-(x-3))/(2(x-2)) - 1/(x-2) + 1 = 0}}} Simplify



{{{(-x+3)/(2(x-2)) - 1/(x-2) + 1 = 0}}} Distribute the negative.




{{{cross(2(x-2))((-x+3)/cross(2(x-2)))+2cross((x-2))((-1)/cross((x-2)))+2(x-2)(1)=2(x-2)(0)}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{2(x-2)}}}. Doing this will eliminate all of the fractions.



{{{-x+3+2(-1)+2(x-2)=0}}} Multiply and simplify.



{{{-x+3-2+2x-4=0}}} Distribute.



{{{x-3=0}}} Combine like terms on the left side.



{{{x=0+3}}} Add {{{3}}} to both sides.



{{{x=3}}} Combine like terms on the right side.



----------------------------------------------------------------------


Answer:


So the answer is {{{x=3}}}