Question

How do you simplify the rational expression and state any restrictions on the variable `(b^2 +6b-16)/(b+8)`?

Answer 1

Extract a factor equal to the denominator from the numerator (note this is not always possible in every case, but it works in this example) and simplify.

Remember that, as a restriction, division by `0` is invalid.

`(b^2+6b-16)/(b+8)`

`= ((b-2) cancel(b+8))/(cancel(b+8))` provided `b+8 != 0`

`(b^2+6b-16)/(b+8) = b-2`

provide `b!= (-8)`

Answer 2

The answer is `(b-2)`.

Beginning Equation:

`(b^2+6b-16)/(b+8)`

Factor the numerator.

`((b-2)(b+8))/(b+8)`

Cancel (b+8) from the numerator and denominator.

`((b-2)cancel(b+8))/cancel(b+8)`

That leaves `(b-2)`.