The SAT gives you two fractions with variables underneath and asks which single fraction they equal. The process is the same as with numbers: find a common denominator, rewrite both pieces, then combine the numerators. The subtraction version is where most points are lost.
Start simple. To combine 3 over x plus 2 over y, the common denominator is x times y. Rewrite the first fraction as 3y over xy and the second as 2x over xy, then add the numerators to get 3y plus 2x, all over xy. You never touch the denominator once it is common. All the work happens on top.
When denominators share a factor, use the least common denominator rather than the product. For 1 over the quantity x minus 3 plus 4 over the quantity x times the quantity x minus 3, the least common denominator is x times the quantity x minus 3. The first fraction needs a factor of x on top and bottom, becoming x over x times the quantity x minus 3. Adding gives x plus 4 over x times the quantity x minus 3.
Subtraction requires parentheses around the entire second numerator. To compute 5x over 4 minus the quantity x minus 3 over 4, write the numerator as 5x minus the quantity x minus 3, which expands to 5x minus x plus 3, giving 4x plus 3 over 4. Distributing the minus to only the x would give 4x minus 3, and that wrong version will be an answer choice.
Factor before you look for a common denominator, because factoring often reveals that one denominator already contains the other. An expression like x squared minus 9 factors into the quantity x minus 3 times the quantity x plus 3, so a second fraction with denominator x plus 3 needs only one extra factor rather than a full multiplication.
The restrictions printed in the question, such as x not equal to 3, mark the values that would make a denominator zero. They do not change any step of the algebra, but they are a useful hint about what the denominators factor into, and they tell you which candidate solutions would have to be discarded if the question were an equation rather than a simplification.