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

Feb 5, 2018

Let's try factoring everything

$\frac{4 x \left(4 x - 1\right)}{3 - x}$

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 $x = 3$

Feb 5, 2018

$\frac{4 x \left(4 x - 1\right)}{3 - x} \to \left(x \ne 3\right)$

#### Explanation:

$\text{factorise numerator by taking out a "color(blue)"common factor of 4x}$

$= \frac{4 x \left(4 x - 1\right)}{3 - x}$

$\text{the denominator cannot equal zero as this would make}$
$\text{the rational function undefined. Equating the }$
$\text{denominator to zero and solving gives the value that x }$
$\text{cannot be}$

$\text{solve "3-x=0rArrx=3larrcolor(red)"excluded value}$