How do you simplify #(x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)#?

1 Answer
Don H.
May 2, 2018

Invert the divisor polynomial, then multiply (factor) and simplify.
#(a/b)/(c/d) = (a/b) * (d/c) = (a*d) / (b*c)#

Explanation:

#(x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)=# ,invert the divisor and multiply

#(x^2-9)/(x+2)*(x^2-4)/(x^2+x-6)=#

#((x^2-9) * (x^2-4)) / ((x+2)*(x^2+x-6))=# ,then factor and reduce

#((x+3)(x-3)(x+2)(x-2)) / ((x+2)(x+3)(x-2))=#

#((cancel(x+3)) (x-3) (cancel(x+2)) (cancel(x-2))) / (cancel((x+2))cancel((x+3)) cancel((x-2)))=#

#x-3#

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