sums and differences of rational algebraic expression answer the following perform the indicated operation reduce answers to lowest term 2x/x^2-2x-15 - x-2/3x^2+9 another is t/2rs^2 - 2r/3rst + 3s/30r^2t another is 3x/2x-3 - 2x/2x+3 + 3/4x^2-9 please answer this i need it tomorrow morning 3:00 please answer it i will WAIT FOR IT!

To solve the given rational algebraic expressions, we need to perform the indicated operations and then simplify the answers to their lowest terms. Let's solve each expression step by step.

1. Expression: (2x/(x^2-2x-15)) - ((x-2)/(3x^2+9))

First, factorize the denominators:
x^2 - 2x - 15 = (x - 5)(x + 3)
3x^2 + 9 = 3(x^2 + 3)

Now, find the least common denominator (LCD) for the two fractions. The LCD is the product of the factors that appear in the denominators, taken with their highest powers:

LCD = (x - 5)(x + 3)(3)

Next, rewrite each fraction with the LCD as the common denominator:

(2x * 3) / LCD - ((x-2) * (x - 5)) / LCD

Simplifying further:
(6x - 3(x - 5)) / LCD

Expand and combine the like terms:
(6x - 3x + 15) / LCD

Simplify:
(3x + 15) / ((x - 5)(x + 3)(3))
Now we're done with the first expression.

2. Expression: (t / (2rs^2)) - (2r / (3rst)) + (3s / (30r^2t))

We can simplify each fraction by factoring the denominators:

t / (2rs^2) = t / (2rs^2)
2r / (3rst) = 2r / (3rst)
3s / (30r^2t) = s / (10r^2t)

The denominators are already in their simplest form, so we can proceed to combine the fractions:

t / (2rs^2) - (2r / (3rst)) + (3s / (30r^2t))
= t / (2rs^2) - 2r / (3rst) + s / (10r^2t)

To operate on these fractions, we need to find a common denominator, which in this case is 30r^2s^2t. So, we'll now rewrite each fraction with the common denominator:

[t * (15rst)] / (2rs^2 * 15rst) - [2r * (10r^2s^2t)] / (3rst * 10r^2s^2t) + [s * (3r)] / (10r^2t * 3r)

Now, simplify each fraction:

15rt / (30r^2s^2t) - 20r^3s^2t / (30r^2s^2t) + 3rs / (30r^2t)

Combining the fractions, we have:

(15rt - 20r^3s^2t + 3rs) / (30r^2s^2t)

Now, let's simplify further if possible, but there are no common factors in the numerator and denominator. Thus, our final answer is:

(15rt - 20r^3s^2t + 3rs) / (30r^2s^2t)

3. Expression: (3x / (2x-3)) - (2x / (2x+3)) + (3 / (4x^2-9))

Factorize the denominators:
2x - 3 = (2x - 3)
2x + 3 = (2x + 3)
4x^2 - 9 = (2x - 3)(2x + 3)

Now, find the least common denominator (LCD) for the three fractions, which is the product of the factors that appear in the denominators, taken with their highest powers:

LCD = (2x - 3)(2x + 3)

Rewrite each fraction with the LCD as the common denominator:

(3x * (2x + 3)) / (LCD) - (2x * (2x - 3)) / (LCD) + (3) / (LCD)

Simplify each fraction:

(6x^2 + 9x) / (LCD) - (4x^2 - 6x) / (LCD) + (3) / (LCD)

Combine like terms, adding or subtracting the fractions:

[(6x^2 + 9x) - (4x^2 - 6x) + 3] / (LCD)

Simplifying the numerator:

6x^2 + 9x - 4x^2 + 6x + 3 / (LCD)

Combine like terms:

2x^2 + 15x + 3 / (LCD)

The numerator cannot be simplified further, so our final answer is:

(2x^2 + 15x + 3) / ((2x - 3)(2x + 3))

Now, you have the solutions to all three given rational algebraic expressions.