How do you subtract #\frac { 1} { x ^ { 2} - x - 12} - \frac { 1} { x ^ { 2} - 6x + 8}#?

1 Answer
Pankaj Solanki
Sep 20, 2017

#-5/((x-4)(x+3)(x-2))#

Explanation:

#1/(x^2-x-12)-1/(x^2-6x+8)#
#=1/((x-4)(x+3))-1/((x-4)(x-2))#
#=1/(x-4)[1/((x+3))-1/((x-2))]#
#=1/(x-4)[((x-2)-(x+3))/((x+3)(x-2))]#
#=1/(x-4)[(-5)/((x+3)(x-2))]#
#=-5/((x-4)(x+3)(x-2))#

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