Question

Simplify the rational expression below. When typing your numerator and denominators be sure to but the term with the variable first and do not put spaces between your characters. \frac{\left(6a^2-24a+24\right)}{\left(6a^2-24\right)} The numerator is AnswerThe denominator is Answer

Answer 1

We want to simplify the expression:

$\frac{6a^2-24a+24}{6a^2-24}$

We could simplify this equation factoring its denominator and its numerator.

First, let's factor the numerator as follows:

$6a^2-24a+24$

Start multiplying and dividing the equation by 6 and then re-write it as:

$\frac{6(6a^2-24a+24)}{6}=\frac{(6a)^2-24(6a)+144}{6}$

Now, we're going to ask two numbers, whose sum is -24 and its multiplication is 144.

These numbers are -12 and -12. We can put these numbers in our previous equation like this:

$\frac{(6a-12)(6a-12)}{6}$

Now, we could apply common factor to this expression:

$\frac{6(a-2)(6a-12)}{6}=(a-2)(6a-12)$

And, we're going to simplify the denominator of the rational expression applying common factor too and then using the square difference expression like this:

$(6a^2-24)=6(a^2-4)=6(a+2)(a-2)$

Finally, our rational expression can be simplified as:

$\frac{6a^2-24a+24}{6a^2-24}=\frac{6(a-2)(a-2)}{6(a+2)(a-2)}=\frac{a-2}{a+2}$

Therefore, the answers are:

- The numerator is a-2

- The denominator is a+2