divide and simplify
a-b/2a divide a^2-b^2/8a^3
To divide and simplify the expression (a - b) / (2a), and (a^2 - b^2) / (8a^3):
Let's break down the steps for each expression:
Expression 1: (a - b) / (2a)
Step 1: Expand the denominator.
=> (a - b) / (2 * a)
Step 2: Divide the numerator by the denominator.
=> a / (2 * a) - b / (2 * a)
Step 3: Simplify the fractions by canceling out common factors.
=> 1/2 - b / (2 * a)
Expression 2: (a^2 - b^2) / (8a^3)
Step 1: Factor the numerator (difference of squares).
=> [(a + b)(a - b)] / (8a^3)
Step 2: Expand the denominator.
=> [(a + b)(a - b)] / (8 * a * a * a)
Step 3: Cancel out common factors from the numerator and denominator.
=> (1/8) * (a + b) * (a - b) / (a^2)
So, the simplified expressions are:
(a - b) / (2a) = 1/2 - b / (2 * a)
(a^2 - b^2) / (8a^3) = (1/8) * (a + b) * (a - b) / (a^2)