Question

How do you simplify `(3x-12)/(x²-3x-18)- ( x-4)/(x-6)^2`?

Answer 1

`[(x-4)(2x-21)]/[(x+3)(x-6)^2]`

Explanation:

`(3x-12)/(x^2-3x-18)-(x-4)/(x-6)^2`

=`(3*(x-4))/((x+3)*(x-6))-(x-4)/(x-6)^2`

=`(x-4)/(x-6)*[3/(x+3)-1/(x-6)]`

=`(x-4)/(x-6)*[3(x-6)-(x+3)]/[(x+3)(x-6)]`

=`[(x-4)(2x-21)]/[(x+3)(x-6)^2]`