How do you solve #\frac { x - 3} { 2x - 4} = \frac { x } { x - 2} + 2#?

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Answer 1 · 2016-10-27T19:10:15

#x=1#

Solving the rational equation is computed by finding same denominator for denominators in both sides of the equation

Then,
#if color(red)(a/c=b/c# then #color(red)(a=c#

Then common denominator is the #L.C.M(2x-4,x-2)#
#color(blue)(2x-4=2(x-2)#
then #color(blue)(2x-4)# is the common denominator

#rArr(x-3)/(2x-4)=(color(blue)2x)/(color(blue)2(x-2))+(2xxcolor(blue)(2(x-2)))/color(blue)(2(x-2))#

#rArr(x-3)/(2x-4)=(2x+4(x-2))/(2x-4)#

#rArr(x-3)/(2x-4)=(2x+4x-8)/(2x-4)#

#rArr(x-3)/(2x-4)=(6x-8)/(2x-4)#

Then
#color(red)(x-3=6x-8)#

#rArrx-6x=3-8#

#rArr-5x=-5#
#rArrx=(-1)/(-1)#

Therefore, #x=1#