I posed these one's before but added parenthesis which I think made it confusing as the actually questions do not have them. So, I'm reposting them without to see if it makes sense. If not I understand.

1. Compute as indicated. Write your answer in lowest terms. a+3/a^2-4-a+5/a^2-4a+4

a. -6a-16/(a+2)(a-2)^2
b. -6a+4/(a+2)(a-2)^2
c. -6a-16/(a+2)(a-2)
d. -6a+4/(a+2)^2(a-2)

2. Use the properties of exponents to simplify the expression. Write the answer using positive exponents only. So the equation is in parenthesis. (a*b^-4/c^-7)^-3

a. ab^12/c^21
b. b^12/a^3c^21
c. b^12c^7/a^3
d. ab^12c^7

3. Compute as indicated. Write your answer in lowest terms. So this one starts with 3/m-8 then at the end next to the divide line it shows -5. The answer for A start with a negative next to the divide line.

a. - 2/m-8
b. -5m-5/m-8
c. -5m-37/m-8
d. -5m+43/m-8

4. Simplify the compound rational expression. Use either method. So this equation has a +1 before the top equation and a +y before the bottom.
+1 5/y-10/ +y 25/y-10

a. 1/y-5
b. 1/y+5
c. 6/y+25
d. 1/y+1/5

5. Simplify the compound rational expression. Use either method. 2/a-1/3/4/a^2-1/9

a. a+3/3
b. a-3/3
c. 3a/6+a
d. 3a/6-a

6. Compute as indicated. Write final results in lowest terms. x^2+2x-15/2x-6 Divide by x^2-25/4x^2

a. 2x^2/x-3
b. 2x^2/x+3
c. 2x^2/x-5
d. x-5/2x^2

Thanks again for all the help its helping me!

I need help in answering this problem,16

------ . 3
39 ------
10

to the lowest term

1. To compute the expression a+3/a^2-4 - a+5/a^2-4a+4, we can start by finding a common denominator for both fractions. The denominators are (a^2-4) and (a^2-4a+4), which can be factored as (a-2)(a+2) and (a-2)^2 respectively.

Now, we can rewrite the expression using the common denominator. The first fraction, a+3/a^2-4, needs to be multiplied by (a-2)(a+2)/(a-2)(a+2) to obtain the common denominator. Similarly, the second fraction, a+5/a^2-4a+4, needs to be multiplied by (a-2)^2/(a-2)^2.

After expanding and simplifying the expression, we get (-6a-16)/(a+2)(a-2)^2. Therefore, the answer is option (a) -6a-16/(a+2)(a-2)^2.

2. To simplify the expression (a*b^-4/c^-7)^-3, we can start by using the property that states (a/b)^n = a^n/b^n.

Applying this property, we can rewrite the expression as (a^-3*b^12/c^21). Now we can remove the negative exponents by moving the terms to the opposite positions in the fraction.

So, the simplified expression becomes (b^12/a^3c^21). Therefore, the answer is option (b) b^12/a^3c^21.

3. Given the expression 3/(m-8) - 5, we can start by finding a common denominator for the fractions. The first fraction has a denominator of (m-8), so we need to multiply both the numerator and denominator of the second fraction by (m-8) to obtain a common denominator.

After simplifying, we get (3-5(m-8))/(m-8) = (-5m-37)/(m-8). Therefore, the answer is option (c) -5m-37/(m-8).

4. To simplify the compound rational expression, +1(5/y-10) / +y(25/y-10), we can first simplify each individual fraction.

The first fraction, 5/y-10, can be rewritten as (5/(y-10)). The second fraction, 25/y-10, can be simplified to (25/(y-10)).

Now, we can multiply the numerators together and the denominators together: [1 * 5 * 25]/[(y-10) * (y-10)]. Simplifying, we get 125/(y-10)^2.

Therefore, the answer is option (c) 6/(y+25).

5. To simplify the compound rational expression 2/(a-1/3) / (4/(a^2-1/9)), we need to start by simplifying each individual fraction.

The first fraction, 2/(a-1/3), can be written as (6/3)/(a-1/3), which simplifies to 6/(3a-1).

The second fraction, (4/(a^2-1/9)), can be simplified to (4/(a+1/3)(a-1/3)), which is equivalent to 4/(a^2-1/9).

Now, we can divide the two fractions by multiplying the first fraction by the reciprocal of the second fraction: (6/(3a-1)) * ((a^2-1/9)/4).

Expanding and simplifying, we get (3(a+1)(a-1))/2(a-1)(a+1). Canceling out the common factors, we are left with 3/2.

Therefore, the answer is option (a) (a+3)/3.

6. To compute the expression (x^2+2x-15)/(2x-6) divided by (x^2-25)/(4x^2), we can start by simplifying each fraction.

The first fraction, (x^2+2x-15)/(2x-6), can be factored as [(x+5)(x-3)]/[2(x-3)]. The second fraction, (x^2-25)/(4x^2), can be factored as [(x+5)(x-5)]/[4(x)(x)].

Now, we can rewrite the expression as [(x+5)(x-3)]/[2(x-3)] * [4(x)(x)]/[(x+5)(x-5)]. By canceling out the common factors, we get 2x/(x-5).

Therefore, the answer is option (b) 2x^2/(x+3).