How do you simplify #(2x^2-12x)/(x^2-7x+6)div(2x)/(3x-3)#?

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Answer 1 · 2016-10-17T22:14:10

The expression simplifies to #3#, with restrictions being #x!= 6, 1 and 0#.

Turn into a multiplication and factor.

#=(2x^2 - 12x)/(x^2 - 7x + 6) xx (2x)/(3x - 3)#

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

#=3#

Finally, let us note the restrictions on the variable. These are found by setting the denominator to #0# and solving.

#x^2 - 7x + 6 = 0#

#(x - 6)(x - 1) = 0#

#x = 6 and 1#

AND

#3x- 3 = 0#

#3(x - 1) = 0#

#x = 1#

AND

#2x = 0#

#x = 0#

Hence. #x!=6, 1, 0#.

Hopefully this helps!