Question

How do you simplify `(z^2-z-6)/(z-6) *( z^2-6z)/(z^2+2z-15)`?

Answer 1

`(z^2-z-6)/(z-6)*(z^2-6z)/(z^2+2z-15)=(z^2+2z)/(z+5)`

Explanation:

`(z^2-z-6)/(z-6)*(z^2-6z)/(z^2+2z-15)`
`color(white)("XXXX")`Combining the numerator factors and the denominator factors:
`=((z^2-z-6)(z^2-6z))/((z-6)(z^2+2z-15))`
`color(white)("XXXX")`Factoring
`= ((z-3)(z+2)(z)(z-6))/((z-6)(z+5)(z-3))`
`color(white)("XXXX")`Cancelling out matching terms in the numerator and denominator
`= (cancel((z-3))(z+2)(z)cancel((z-6)))/(cancel((z-6))(z+5)cancel((z-3)))`
`color(white)("XXXX")`Rewrite simplified:
`=(z^2+2z)/(z+5)`