What is the quotient of the rational expression x^2+5x+6/x-6 divided by x^2-9/2x-12? Also, it needs to be in reduced form.

Question

anonymous · Answer

Is it :
$$\frac{ x^2+5x+6}{x-6}\div \frac{x^2-9}{2x-12}$$
???

anonymous · Answer

@Noura11 yes I apologize, I didnt know how to create an equation on here.

anonymous · Answer

All you need is to factor some expressions you have !
Can you factor 
$$x^2+5x+6$$ ?

anonymous · Answer

I having a hard time understanding what to factor

anonymous · Answer

It is very simple !
Look !
The expression :
$$ x^2+5x+6$$
can be factored like this :
$$x^2+5x+6=(x+a)(x+b)$$
where a and b are two numbers such that :
$$a+b=5\text{ and } a\times b=6$$
We can easily say that :
$$2+3=5\text{ and } 2\times 3=6$$
So : a=2 and b=3 (or the inverse !!!)
So :
$$ x^2+5x+6=(x+2)(x+3)$$

anonymous · Answer

so the answer would be 2(x+2)/(x-3) correct?

anonymous · Answer

Yes ! Exactly !

anonymous · Answer

and that is also in reduced form correct?

anonymous · Answer

yes