How do you simplify #2/(x-2) - 3/(x-1)#?

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Answer 1 · 2016-02-15T00:39:03

Use multiplication by #1# to make the denominators the same to find

#2/(x-2)-3/(x-1) =(-x+4)/((x-1)(x-2))#

#2/(x-2)-3/(x-1) = 2/(x-2)*color(red)(1)-3/(x-1)*color(red)(1)#

#=2/(x-2) * color(red)((x-1)/(x-1))-3/(x-1)*color(red)((x-2)/(x-2))#

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

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

#=(2x-2-3x+6)/((x-1)(x-2))#

#=(-x+4)/((x-1)(x-2))#