2s + s
-- ---
s^2 s-1
Add & Simplify
To add and simplify the expression (2s + s) / (s^2 - (s-1)), we first need to find the least common denominator (LCD) for the two fractions. The LCD is the smallest multiple of the denominators s^2 and s-1.
To find the LCD, we factor the denominators:
s^2 = s * s
s-1 = (s - 1)
Since there are no common factors between the two denominators, the LCD is the product of both denominators: s^2 * (s - 1).
Now, let's write the expression with the common denominator:
(2s * (s - 1) + s * s^2) / (s^2 * (s - 1))
Next, we simplify the numerator. Distribute the 2s across (s - 1):
(2s^2 - 2s + s^3) / (s^2 * (s - 1))
Finally, we have the simplified expression:
(s^3 + 2s^2 - 2s) / (s^2 * (s - 1))
Therefore, the simplified expression is (s^3 + 2s^2 - 2s) / (s^2 * (s - 1)).