Question

Simplify the expression (b^(-5/2)b) * (b² - 3b) / (b - 5):

a) b³
b) b^(5/2) - 3b^(3/2)
c) b^(3/2) - 3b
d) b^(3/2) - 3b^(5/2)

Answer 1

To simplify the expression (b^(-5/2)b) * (b² - 3b) / (b - 5), combine the exponents of b, expand the expression, and divide by (b - 5) to get b^(-3/2) - 3b^(1/2).

Step-by-step explanation:

To simplify the expression (b-5/2b) * (b² - 3b) / (b - 5), we can follow these steps:

1. Combine the exponents of b-5/2 and b to get b-5/2 + 1 = b-3/2.
2. Expand the expression (b² - 3b) to get b² - 3b.
3. Divide (b-3/2 * (b² - 3b)) by (b - 5) to get b-3/2 - 3b1/2.

Therefore, the simplified expression is b-3/2 - 3b1/2, which corresponds to option (c)