simplify the fraction ((4t^2-16)/8)/((t-2)/6)
I'm having trouble solving it.
I got 3(t+2)
(4(t^2-4)/8) / ((t-2)/6)
(t-2)(t+2)/2 * 6/(t-2)
3(t+2)
you are correct
To simplify the given fraction, you can follow these steps:
Step 1: Simplify each part separately.
Start by simplifying the numerator and denominator separately.
Numerator: (4t^2 - 16)
We can factor out a common factor of 4:
4t^2 - 16 = 4(t^2 - 4)
Now, we apply the difference of squares formula to further simplify the numerator:
t^2 - 4 = (t - 2)(t + 2)
Therefore, the numerator becomes: 4(t - 2)(t + 2)
Denominator: (t - 2)
No further simplification is needed for the denominator.
Step 2: Simplify the entire fraction.
Now, we have the simplified numerator and denominator:
Numerator: 4(t - 2)(t + 2)
Denominator: (t - 2)
To simplify the entire fraction, we can cancel out the common factor of (t - 2):
4(t - 2)(t + 2) / (t - 2)
Canceling out (t - 2), we are left with:
4(t + 2)
So, the simplified fraction is: 4(t + 2)