# Math Help - Rational function operations

1. ## Rational function operations

$\frac{x-4}{6x-24}$÷ $\frac{1}{4-x}$ = ?

Result:
$\frac{(x-4)(4-x)}{6x-24}$

I do not know if I should simplify this...

2. ## Re: Rational function operations

Originally Posted by vaironxxrd
$\frac{x-4}{6x-24}$÷ $\frac{1}{4-x}$ = ?

Result:
$\frac{(x-4)(4-x)}{6x-24}$

I do not know if I should simplify this...
Yes you should...

\displaystyle \begin{align*} \frac{(x - 4)(4 - x)}{6x - 24} &= \frac{(x - 4)(4 - x)}{6(x - 4)} \\ &= \frac{4 - x}{6} \end{align*}

3. ## Re: Rational function operations

Oops. I was a little too late. Lol.

4. ## Re: Rational function operations

One "technical point":
$\frac{(x- 4)(4- x)}{6(x- 4)}= \frac{4- x}{6}= -\frac{x- 4}{6}$
for $x\ne 4$.

It is not defined for x= 4.