Question 74431
1. (x+8)(3x-1)+(x+3)(x+1)
First, multiply the two binomial sets.
(3x^2-x+24x-8)+(x^2+x+3x+3)
Combine any like terms in the parentheses
(3x^2+23x-8) +(x^2+4x+3)
Drop the parentheses. Because there is an addition sign between the two sets of parentheses, there will be no sign changes in the second set of parentheses.
3x^2+23x-8+x^2+4x+3
Combine like terms
-5x^2+27x-5
To avoid confusion, you can also rewrite the expression with the like terms beside each other.

2.  4/(x+4) - 7/5x
First, you must make both "fractions" have a common denominator. You do this by multiplying the first by 5x/5x and the second by (x+4)/(x+4). That is the same thing as multiplying both of them by 1. This gives you an equivalent fraction for each one of them.
(5x/5x)(4/x+4)-(x+4)/(x+4)(7/5x)
Multiply them out.
(20x/5x^2+20x) - (7x+4/5x^2+20x)
Now that they have a common denominator, you can put the numerators together.
Note that the minus sign between the two fractions causes both the 7x and the 4 to be negative.
20x-7x-4/5x^2+20x
Combine like terms in the numerator. 
13x-4/5x^2+20x

3. 4x/(5x-2) - 2x/(5x+1) 
You will do the same thing with this expression, giving both fractions a common denominator. This will be done by multiplying the first fraction by (5x+1)/(5x+1) and the second one by (5x-2)/(5x-2).
(5x+1)/(5x+1)(4x/5x-2)-(5x-2)/(5x-2)(2x/5x+1)
Multiply them out.
(20x^2+4x/(25x^2-10x+5x-2)-(10x^2+4)/25x^2-10x+5x-2)
Combine the like terms in the denominators.
(20x^2+4/25x^2-5x-2)-(10x^2+4)/25x^2-5x-2)
Now that they have a common denominator, you can put the numerators together.
Note that the minus sign between the two fractions causes 10x^2 and the 4 to be negative.
20x^2+4x-10x^2-4x/25x^2-5x-2
Combine like terms in the numerator.
10x^2/25x^2-5x-2