Question

How do you simplify and find the excluded values of `(16x^2 - 4x)/(3 - x)`?

Answer 1

Let's try factoring everything

`(4x(4x-1))/(3-x)`

It looks like there are no common factors here, so we can't simplify it

However, there are still excluded values. These are any values of `x` that make the denominator `0` (we can't have that, because that would be dividing by `0`).

So let's set `3-x` equal to `0` and solve for `x`

`3-x = 0`

`-x=-3`

`x=3`

So the excluded value for this expression is `x=3`

Answer 2

`(4x(4x-1))/(3-x)to(x!=3)`

Explanation:

`"factorise numerator by taking out a "color(blue)"common factor of 4x"`

`=(4x(4x-1))/(3-x)`

`"the denominator cannot equal zero as this would make"`
`"the rational function undefined. Equating the "`
`"denominator to zero and solving gives the value that x "`
`"cannot be"`

`"solve "3-x=0rArrx=3larrcolor(red)"excluded value"`