Question

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

Answer 1

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`