(t-2)/(t+4) x (4t+16)/(2t^2-8)
Ok, your common denominator is
2(t+4)(t-2)(t+2)
lots of factoring here, and lots of canceling.
(t-2)/(t+4) x 4(t+4)/[2(t-2)(t+2)]
= 2/(t+2), where t is NOT equal to 2,-4
Most likeylBob saw your x as a +
Thank you so much.
To simplify the given expression (t-2)/(t+4) * (4t+16)/(2t^2-8), we can follow the steps:
Step 1: Factorize the expressions
In the first expression (t-2)/(t+4), there are no common factors that can be factored out.
In the second expression (4t+16)/(2t^2-8), we can factor out 4 from the numerator and denominator: (4(t+4))/(2(t^2-4))
Step 2: Simplify the expression
Now, the expression becomes (t-2)/(t+4) * (4(t+4))/(2(t^2-4))
Step 3: Cancel out common factors
In the first expression (t-2)/(t+4) and the numerator of the second expression 4(t+4), we have a common factor of (t+4). Cancel out this common factor.
The expression simplifies to (t - 2)/(1) * (4)/(2(t^2 - 4))
Step 4: Simplify further
Now, we can simplify the expression by multiplying the numerators and denominators together:
(t - 2) * (4) / (2(t^2 - 4) * 1)
Simplifying the denominator: 2(t^2 - 4) * 1 = 2t^2 - 8
Final simplified expression:
4(t - 2) / (2t^2 - 8)
Therefore, the simplified expression is 4(t - 2) / (2t^2 - 8).