How do you simplify the rational expression: (x-3)/(x^2-5x+6)#?

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Answer 1 · 2018-06-08T08:21:22

#1/(x-2)#

Simply the #x^2-5x+6# first:

Lets find the factors of #x^2-5x+6#

#3 xx 2 = 6# ----> adding them gives #5# ----> we want adding it gives #-5#

#-3 xx -2 = 6# ----> adding them gives #-5# ---> This is the one.

Re-write the equation as follows:

#x^2-5x+6#

#x^2-3x-2x + 6#

#x(x-3)-2(x-3)#

#(x-2)(x-3)#

So now we have;

#(x-3)/(x^2-5x+6)# = #(x-3)/((x-2)(x-3))# = #cancel(x-3)/((x-2)cancel((x-3))# = #1/(x-2)#

Hence its simplified as:

#(x-3)/(x^2-5x+6)# = #1/(x-2)#