simplify the rational expression, state any restrictions on the variable...t^2+t-6/t^2-9

Question

nnesha · Answer

factor numerator and denominator

nnesha · Answer

$$\huge\rm (a^2 -b^2) = (a+b)(a-b)$$
difference of square 
apply that at the denominator

anonymous · Answer

t-2/t-3 t=3 t=-3? is what i got for the final

nnesha · Answer

t^2 + t - 6
what are factors of this equation ?

anonymous · Answer

3

nnesha · Answer

just 3 ?

anonymous · Answer

i mean you could go 2,3 6

anonymous · Answer

so my answer up there wasnt right?

nnesha · Answer

3 times -2 =  -
and 3-2= 1
that would be factor of t^2 + t -  6 :-)

nnesha · Answer

yes that's right

nnesha · Answer

t = 3 t = -3 ??? explain this plz

anonymous · Answer

So its the right choice? explain what?

anonymous · Answer

My brother just told me he thinks that was right, he didnt explain

nnesha · Answer

so you don't know how to solve it ?

anonymous · Answer

No sir, He just said i think its that one, no explaining at all. i would like to know how to though.

nnesha · Answer

t^2 +t -6
find two number if you multiply them you should get -6
and if you add or subtract them you should get middle term which is one

anonymous · Answer

why is it not 3, -2?

nnesha · Answer

who said it's not ?

anonymous · Answer

haha, okay, but those two should give us that

nnesha · Answer

it is so bec leading coefficient is 1 just write it as ( t+ 3) and (t-2)
this is the numerator $$\frac{ (t+3)(t-2) }{ ? }$$ 
now denominator 
t^2 - 9 factor it

anonymous · Answer

ok what do you mean? im sorry.

anonymous · Answer

oh wait

anonymous · Answer

that one gave me t+3 t-3

nnesha · Answer

^^

nnesha · Answer

$$\huge\rm \frac{ (t+3)(t-2) }{ (t+3)(t-3) }$$ 
simplify

anonymous · Answer

t-2/t-3

nnesha · Answer

ye right now denominator can't be equal to 0
 so tha'ts mean $$\huge\rm t-3 \cancel{=} 0$$
solve for t

anonymous · Answer

=3

nnesha · Answer

not equal

anonymous · Answer

And thats the final answer? :)

anonymous · Answer

i know. just 3 is the restriction

nnesha · Answer

$$\huge\rm t \cancel{=} 3$$
bec if you plug 3 for t
3-3= 0 but we don't like 0 for this question

nnesha · Answer

yes right

nnesha · Answer

gO_Od to go!

anonymous · Answer

If i open another would you help me?  i really appreciate that!! you actually explained. i get that

nnesha · Answer

i'll try :-)