The first thing to remember is the order of operations to solve the problem. The mnemonic device I like to remember the order is
Please Excuse My Dear Aunt
Sally - which stands for Parentheses, Exponents,
Multiplication, Division, Addition, then
Subtraction. So first, you start with what is within the parentheses: 3/5+3/4. To add two fractions, you have to make the denominators (lower parts) of the fractions equal to each other (called finding the lowest common denominator).
The easiest way to find this is to multiply the denominators together. 5 * 4 = 20, so this will be our new denominator. Let's start with the first fraction: 3/5. We got the denominator of 5 to equal 20 by multiplying the bottom number by 4, so now we must also multiply the top of the fraction (3) by 4. 3 * 4 = 12, so the new fraction we are going to use, then, is 12/20. Then we do the same to the second fraction - we multiplied the denominator of 4 by 5 to get the common denominator 20, so now we must do the same to the top number - 3*5=15, so the new fraction is 15/20. Now we take the two fractions we just made, 12/20 and 15/20, and add them together. Since the denominators are now the same, you just have to add the two numerators, and 12+15=27. This makes it so that 3/5 + 3/4 = 12/20 + 15/20 = 27/20.
Now that the parentheses are solved for, you must subtract 1/2 from 27/20. Again, you do this by finding the least common denominator. You can get 20 from 2 by multiplying it by 10, so multiply both the top and bottom of the fraction by 10, which equals 10/20. Now you can subtract: 27/20 - 10/20 = 17/20. The answer is 17/20.