my topic is all about sums and differences of a rational algebraic expression this is the problem 3a/ax+ay + 2a/ax+ay another problem is a/4a+1 + 2/4a^2-7a-2 another is 3/a-b + 4/a+2b please anyone else who can answer my assignment please HELP ME!

((8/4)+6))x2

Sure, I can help you with your assignment on sums and differences of rational algebraic expressions. Let's solve each problem step by step.

Problem 1: Simplify the expression 3a/(ax+ay) + 2a/(ax+ay)

To solve this problem, we need to find a common denominator for the fractions. The common denominator in this case is (ax+ay).

1. Start by rewriting each term with the common denominator:
3a/(ax+ay) + 2a/(ax+ay)

2. Combine the numerators over the common denominator:
(3a + 2a)/(ax+ay)

3. Simplify the numerator:
5a/(ax+ay)

Therefore, the simplified expression is 5a/(ax+ay).

Problem 2: Simplify the expression a/(4a+1) + 2/(4a^2-7a-2)

We will follow the same steps as before to solve this problem.

1. Start by rewriting each term with the common denominator. In this case, there doesn't appear to be a common denominator, so we need to factor the denominators.

a/(4a+1) + 2/(4a^2-7a-2)
The denominator 4a^2-7a-2 can be factored as (4a+1)(a-2).

So, we can now rewrite the expression as:
a/(4a+1) + 2/[(4a+1)(a-2)]

2. Now, we can find a common denominator for the fractions:
The common denominator is (4a+1)(a-2).

Rewriting each term with the common denominator:
a(a-2)/[(4a+1)(a-2)] + 2/[(4a+1)(a-2)]

3. Combine the numerators over the common denominator:
(a(a-2) + 2)/[(4a+1)(a-2)]

4. Simplify the numerator:
(a^2 - 2a + 2)/[(4a+1)(a-2)]

Therefore, the simplified expression is (a^2 - 2a + 2)/[(4a+1)(a-2)].

Problem 3: Simplify the expression 3/(a-b) + 4/(a+2b)

We will again follow the same steps to solve this problem.

1. There doesn't seem to be a common denominator initially, so we will leave it as it is:
3/(a-b) + 4/(a+2b)

2. Since we cannot simplify further by finding a common denominator, we leave it as it is.

Therefore, the simplified expression is 3/(a-b) + 4/(a+2b).

Please note that it's always a good practice to check for any factoring or additional simplifications that can be done.