How do you solve #2/3 = 2 - (5x-3)/(x-1)#?

1 Answer
Jul 12, 2016

Answer:

#x = 5/11#

Explanation:

#2/3 = 2 - (5x-3)/(x-1)#

In an equation with fractions, we can get rid of denominators completely by multiplying by the LCM of the denominators. Then the denominators can cancel.

In this case the LCM = #color(red)(3(x-1))#

#(color(red)(3(x-1))xx 2)/3 = color(red)(3(x-1))xx2 - (color(red)(3(x-1))xx(5x-3))/(x-1)#

#(cancel3(x-1)xx 2)/cancel3 = 6(x-1) - (3cancel(x-1)xx(5x-3))/cancel(x-1)#

#2(x-1) = 6(x-1) - 3(5x-3)#

#2x-2 = 6x-6-15x+9#

#2x-6x+15x = -6+9+2#

#11x = 5#

#x = 5/11#