What is the quotient of (t+3)/(2t) divided by (2t+6)/(t-4)?

Question

blurbendy · Answer

It looks like this?
$$\frac{ t + 3 }{ 2t }     /      \frac{ 2t -6 }{ t-4 }$$

blurbendy · Answer

/ means "divide"

anonymous · Answer

Yeah!

anonymous · Answer

@blurbendy I set it up with the right hand side as the inverse so that I could multiply across, and I was thinking that I solved it down properly, but my answer didn't match any of the answer choices.

blurbendy · Answer

okay, so you did 

$$\frac{ t + 3 }{ 2t } * \frac{ t-4 }{ t2 - 6} ?$$

anonymous · Answer

Yes, and I got (t+3)(t-4)/2t(t-4).

anonymous · Answer

So I wrote it out as (t^2-t-12)/(2t^2-8t)...

blurbendy · Answer

bottom should be 2t(2t +6)

blurbendy · Answer

yeah, i just saw that :)

blurbendy · Answer

thanks chief

blurbendy · Answer

do you see why the bottom is 2t(2t+6) @tasteless-teens ?

anonymous · Answer

Can you see this attachment?

blurbendy · Answer

yes, so you factored the top right when you got:
(t+3)(t-4)

the bottom is 2t(2t + 6) = 4t^2 + 12t
= 4t(t + 3)

= (t + 3) (t-4) / 4t(t+3)

Do you see anything that can cancel out?

anonymous · Answer

the t+3

blurbendy · Answer

yes, so what does your answer become

anonymous · Answer

t-4/4t

blurbendy · Answer

good job!

anonymous · Answer

Wow, I really confused myself on that. Thank you! XD

blurbendy · Answer

yw

anonymous · Answer

Wait, so t does not equal 0 and 4, or t does not equal -3, 0, and 4?

blurbendy · Answer

look at your original equation.  if t = 0, then

2(0) = 0 in the denominator which is undefined

if t = 4, then 4 -4 in the denominator of the second expression results in 0 which is also undefined.

anonymous · Answer

So when we set it as 0, t does not equal 4?

anonymous · Answer

And that -3 was irrelevant?

blurbendy · Answer

no, it's saying t can't equal 0 or 4 because if you look at your original equation

if you let t = 0, then

for (t + 3/2t)
(0 + 3) / 2(0) = 3/0 which is undefined

If t = 4, then for
(2t + 6) / (t- 4) 
= 8 +6 / 0 = 14/0 which is undefined

blurbendy · Answer

you never want 0 in the denominator, that's bad.  the answer is the second one, so the one where t = -3 is wrong

anonymous · Answer

I just thought it was strange that the t =-3 was there. Thanks for pointing this out for me.

blurbendy · Answer

np