How do you simplify #(8x-16)/(x^2-13x+22)# and find the restrictions on the variable?

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Answer 1 · 2018-02-11T22:12:39

#8/(x-11);x# cannot be #11#

#-11 - 2 = -13#

#-11 * -2 = 22#

#x^2 - 13x + 22 = (x-11)(x-2)#

#8x - 16 = 8(x-2)#

#(8x-16)/(x^2-13x+22) = (8(x-2))/((x-11)(x-2))#

#= 8/(x-11)#

#n/0 =# undefined

the denominator, #x-11#, cannot be #0#.

this means that #x# cannot be #11#.

graph{8/(x-11) [-17.88, 38.62, -19.63, 9.8]}