Simlify the fraction 4t^2-16/8/t-2/6?

Answer 1

Is this problem supposed to be
[(4t² - 16) / 8] / [(t - 2) / 6] ?
If so, adding the parentheses to show the proper order of divisions is helpful.

Dividing two fractions means multiplying by reciprocals:
[(4t² - 16) / 8] ÷ [(t - 2) / 6]
= [(4t² - 16) / 8] · [6 / (t - 2)]
= 6(4t² - 16) / 8(t - 2)

Factor, cancel common factors, and simplify.
6(4t² - 16) / 8(t - 2)
= 6 · 4(t² - 4) / 8(t - 2)
= 24(t + 2)(t - 2) / 8(t - 2)
= 3(t + 2).

Answer 2

Dangit, Michelle, use parentheses when writing a problem like this on the computer. Strictly following the order of operations (Exponents, Mult/div, Add/Sub), what you have written is (4t^2) - (16/8/t) - (2/6), which gives us 2t^2 - 1/t - 1/3. Now, I'm going to assume some things here (knowing something of how most math books are put together), and say the question is actually...

((4t^2 - 16) / 8 ) / ((t-2)/6)
First, we'll factor the 4 out of the first polynomial, giving us (4(t^2-4)). Since the expression (t^2 - 4) is a special situation called the difference of squares (t^2 - 2^2), we can factor that as (t+2)(t-2), giving us...
((4(t+2)(t-2))/8) / ((t-2)/6)
Now, we get rid of the coefficiant for (t+2)(t-2) by factoring (2*2).../(2*2*2) = 1.../2. Since division is equivalent (the same as) multiplying by a reciprocal, I'll change the / to a * and flip the second fraction.
(((t+2)(t-2))/2) * 6/(t-2)
Now, we combine the two by multiplying numerators and denominators (and factor that 6 for good measure), giving
(2*3*(t+2)*(t-2))/(2*(t-2))
Now, we can get rid of the 2 and the t-2, leaving 3(t+2). Depending on your instructors preference, either that, or 3t+6 is the answer.

Answer 3

if by this you mean

((4t^2 - 16)/8)/((t - 2)/6)
(4(t^2 - 4)/8)/((t - 2)/6)
((t^2 - 4)/2) / ((t - 2)/6)
((t^2 - 4)/2) * (6/(t - 2))
(6(t^2 - 4))/(2(t - 2))
(6/2) * ((t^2 - 4)/(t - 2))
3 * (((t - 2)(t + 2))/(t - 2))

ANS : 3(t + 2) or 3t + 6

Answer 4

(4(t+2)(t-2)/8)*6/t-2
3(t+2)

Answer 5

It simplifies down to "Stop cheating and read your damn math book!"