Final answer:
To find the sum, combine the terms and find a common denominator. The correct answer is 5x-4/(7x-y).
Step-by-step explanation:
To find the sum of the given expression, we need to combine like terms.
The given expression is 5x/(7x-y) + 4/(y-7x).
First, let's simplify each term: 5x/(7x-y) and 4/(y-7x).
Next, we need to find a common denominator for these two terms, which is (7x-y)(y-7x).
Now, we can add the two terms: 5x/(7x-y) + 4/(y-7x) = (5x(y-7x) + 4(7x-y))/((7x-y)(y-7x)).
Therefore, the sum is (5xy-35x^2 + 28x-4y)/((7x-y)(y-7x)).
The correct answer is option c. 5x-4/(7x-y).