How do you simplify #\frac { x ^ { 2} - 13x + 42} { 18- 3x } \cdot \frac { x ^ { 2} - 12x + 36} { x - 6}#?

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Answer 1 · 2017-09-21T08:38:00

Answer = # ((x - 7) (x - 6) ) / (- 3 ) #

or # ((x^2 -13x + 42) ) / (- 3 ) #

# (x^2 - 13x + 42) / (18 - 3x)# x # (x^2 - 12x + 36)/ (x - 6)#

Factorise

= #(x^2 -6x - 7x + 42 ) /(3 (6 - x) )# x # (x^2 -6x -6x + 36)/ ((x-6)#

= #(x(x -6) - 7(x - 6 )) /(3 (6 - x) )# x # (x( x -6) -6(x - 6))/ ((x-6)#

= # ((x-6)(x -7)) / (3 (6-x)# x # ((x-6) (x- 6))/( (x - 6)#

representing #3( 6 - x) # as # - 3(x-6) #

= # ((x-6)(x -7)) / (-3(x-6)# x # ((x-6) (x- 6))/( (x - 6)#

Cancel the like terms in the numerator and denominator

= # ((x -7)) / (-3# x #( (x-6))/ (1)#

= # ((x - 7) (x - 6) ) / (- 3 ) #
or
# ((x^2 -13x + 42) ) / (- 3 ) #