Question

Can I have some help, please?

Answer 1

Answer:

$-3(t+1)(8t-3)$

Step-by-step explanation:

First, factor both the denominators completely:

$9-24t\\= 3(3-8t)\\= 3(-8t+3)\\= -3(8t-3)$

$8t^2+5t-3\\= 8t^2+8t-3t-3\\= 8t(t+1)-3(t+1)\\= (8t-3)(t+1)$

Now, we can see that the factors of the first denominator are -3 and 8t-3.

The factors of the second denominator are t+1 and 8t-3.

To find the LCD, multiply all of these factors together:

$-3(t+1)(8t-3)$

Notice how we only multiply 8t-3 in the equation once. This is because it was present in both denominators, unlike the other factors.

I hope this helps!