Final answer:
To add the fractions (x)/(x-5) and (4x-2)/(x-5), combine the numerators to get (5x-2)/(x-5) since the denominators are already the same.
Step-by-step explanation:
To add the fractions given in the question, you can simply add the numerators because the denominators are the same. The equation is as follows:
(x)/(x-5) + (4x-2)/(x-5) = (x + 4x - 2)/(x - 5).
Combine like terms in the numerator:
(5x - 2)/(x - 5).
This is the simplified form of the added fractions. There is no need to combine denominators or multiply in this case, as often misconceived. Always remember that when dealing with fractions, the denominators should never be added, only the numerators when the denominators are the same.