I really dont get this one help?
x^2-x-6 / 2x^2+x-6

Question

I really dont get this one help?
x^2-x-6 / 2x^2+x-6

anonymous · Answer

factor the top and the bottom. do you know how to factor?

anonymous · Answer

somewhat

anonymous · Answer

alright what would the numerator be factored?

anonymous · Answer

you need two numbers that add to -1 and multipy to get -6

anonymous · Answer

$$x^2-x-6$$

$$?*?=-6,?+?=-1$$

there is another way of doing this if you're stumped. it's more systematic and takes longer, but helps you before you can do coefficient 1 quadratic equations.

anonymous · Answer

would you like me to show you the other way?

anonymous · Answer

yeah please

anonymous · Answer

alright so first take the coefficient of the term

$$x^2$$

the coefficient is 1. next take the constant (the number without x. That number is -6.multiply these numbers.

$$1*-6=-6$$

figure out all the possible combinations to multiply -6

$$1*-6,2*-3,3*-2,6*-1$$

now take these and see which add up to -1

$$1+-6=-5$$
$$2+(-3)=-1$$

as you can see 2 and -3 are the numbers we're looking for. Now take the 2 numbers, multiply them by x and replace the -x in your equation by them. you should get this

$$x^2+2x-3x-6$$

now group the first two and the second two

$$(x^2+2x)+(-3x-6)$$

in each group you can see a common factor for the first it is x for the second it is -3 doing this gets you

$$x(x+2)-3(x+2)$$

when you se x+2 in both parenthesis you know you have done correctly. You only need one x+2 and the outside part

$$(x+2)(x-3)$$

this is the same as your original 

$$x^2-1x-6$$

anonymous · Answer

so now that you know the top is

(x+2)(x-3), think youcan do the bottom? and tell me what you ge

anonymous · Answer

okay let me try it

anonymous · Answer

is it something like 2x-3 ?

anonymous · Answer

yes and the other part of the factor is?

anonymous · Answer

(2x-3)(x+?)

anonymous · Answer

the top part?

anonymous · Answer

when you factored the bottom you grouped, you got something like this correct?

2x(x+?)-3(x+?)

anonymous · Answer

2x-3 is part of the factor but you still needthe (x+?)

anonymous · Answer

you should have got (x+2)(2x-3)

when you put the numerator and denominator together you get

$$\frac{(x+2)(x-3)}{(2x-3)(x+2)}=\frac{x-3}{2x-3}$$