Question

Simplify the expression below.

Answer 1

The first we are going to do to simplify the expression
`(6m^(3)-16m^(2)+15m-40)/(2m^2+5)` is factoring the numerator by grouping similar terms as follows:

`(6m^(3)-16m^(2)+15m-40)/(2m^2+5)`

`((6m^(3)-16m^(2))+(15m-40))/(2m^2+5)`

`(2m^2(3m-8)+5(3m-8))/(2m^2+5)`

`((3m-8)(2m^2+5))/(2m^2+5)`

Now we can cancel the common factor,
`2m^2+5` in both numerator and denominator:

`((3m-8)(2m^2+5))/(2m^2+5)`

`3m-8`

We can conclude that
`(6m^(3)-16m^(2)+15m-40)/(2m^2+5) =3m-8`