the problem is to simplify
(9x^2-12x / x^2+1) * (2x^2+2 / 9x^2+6x-24)
the answer is 2x / x+2
i just have no clue how to reach that conclusion...im really close though...im stuck at
2x(3x-4) / 3x^2+2x-8
any help would be great
thanks
Hello
Just before getting this result, you had something which looked like (otherwise multiply the fraction by )
One can notice that the denominator is the beginning of the development of a square like : . You should try to complete it and see what happens.
ah i totally forgot how to factor quadrilaterals with bigger numbers in front of the x2
the way i did it was to take break it to
then i did and found the two factors of -24 that equal 2, 6 and -4
so i had which factors to
add the 3 in front of it again from the first factor and i got my answer
this is how i remember being taught, but is there a faster/more efficient way to come up with this factor?
and thank you all for the quick help
PS: flyingsquirrel & moo - Im not sure I really understand either of your posts :/ Moo's being the more confusing of the two
(1)
when you look at , you may notice that with and , the beginning of the expression looks like the beginning of (1).
The idea is to complete the square, that's to say to write .
It gives us which brings the simplifications you were looking for.
Using Moo's advice : finding the root(s) of the polynomial and then factoring it. (if and are the two roots of the polynomial, ( allowed) )this is how i remember being taught, but is there a faster/more efficient way to come up with this factor?
I'm sorry about itPS: flyingsquirrel & moo - Im not sure I really understand either of your posts :/ Moo's being the more confusing of the two
It's a method you can understand only if you've already studied it
If you are interested : Solve Quadratic Equations Using Discriminants (1)
Good luck
I see how Moo's method would help me find the roots but I still don't get how after i have the roots i would come up with the factor of the polynomial.
Granted on this problem I dont think I could use that method anyway, considering the test im studying for does not allow calculators and the roots arent the easier numbers to deal with.
If and are the roots of , we have the equality :
Here, the roots were "easy" to calculateGranted on this problem I dont think I could use that method anyway, considering the test im studying for does not allow calculators and the roots arent the easier numbers to deal with.
Hence
But don't use it if you haven't studied it yet, it'd be dangerous for your test