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

1 Answer
Jun 8, 2018

Answer:

#1/(x-2)#

Explanation:

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)#