Question

Perform the indicated operation and simplify the result.

Answer 1

Given:

`$(a-a b)/(a^(2)) / (a-1)/(a^(3))`

Solution:

`$(a-a b)/(a^(2)) / (a-1)/(a^(3))`

Apply the fraction rule:

`$(w)/(x) / (y)/(z)=(w)/(x) * (z)/(y)`

Using this rule,

`$(a-a b)/(a^(2)) / (a-1)/(a^(3))=(a-a b)/(a^(2)) * (a^(3))/(a-1)`

Factor out common term a in first fraction.

`$=(a(1-b))/(a^(2))* (a^(3))/(a-1)`

Cancel the common factor a.

`$=(1-b)/(a) * (a^(3))/(a-1)`

Apply the multiplication of fraction rule:

`$(w)/(x) * (y)/(z)=(w * y)/(x * z)`

Using this rule, we get

`$=((1-b) a^(3))/(a(a-1))`

Cancel the common factor a.

`$=(a^(2)(1-b))/(a-1)`

Therefore,

`$(a-a b)/(a^(2)) / (a-1)/(a^(3))=(a^(2)(1-b))/(a-1)`