To simplify the expression (4x + 2) / (x + 5) – (3x – 1) / (x + 5), we first notice that both fractions have the same denominator, which is (x + 5).
This allows us to combine the numerators directly. So, we can rewrite the expression as:
(4x + 2 – (3x – 1)) / (x + 5)
Now, we simplify the numerator:
4x + 2 – 3x + 1 = (4x – 3x) + (2 + 1) = x + 3
Now, we substitute back into our fraction:
(x + 3) / (x + 5)
This is the simplified form of the original expression. Therefore, the answer is:
(x + 3) / (x + 5)