Question

What is the quotient of `(b-9)/b -: 7/b`?

Answer 1

See the entire solution process below:

Explanation:

First, rewrite the expression as:

`((b-9)/b)/(7/b)`

Next, use this rule for dividing fractions to rewrite the expression again:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(b - 9)/color(blue)(b))/(color(green)(7)/color(purple)(b)) = (color(red)((b - 9)) xx color(purple)(b))/(color(blue)(b) xx color(green)(7))`

Next, cancel common terms in the numerator and the denominator:

`(color(red)((b - 9)) xx cancel(color(purple)(b)))/(cancel(color(blue)(b)) xx color(green)(7)) = (b - 9)/7` Where `7/b != 0` and where `b != 0`