Question

How do you find the quotient of `(n&2+7n+12)/(16n^2)div(n+3)/(2n)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`((n^2 + 7n + 12)/(16n^2))/((n + 3)/(2n))`

Next, use this rule of dividing fractions to rewrite the fraction as:

`(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)((n^2 + 7n + 12))/color(blue)((16n^2)))/(color(green)((n + 3))/color(purple)((2n))) = (color(red)((n^2 + 7n + 12)) xx color(purple)((2n)))/(color(blue)((16n^2)) xx color(green)((n + 3)))`

Next, factor the quadratic as:

`color(red)(((n + 3)(n + 4)) xx color(purple)((2n)))/(color(blue)((16n^2)) xx color(green)((n + 3)`

Then cancel common terms in the numerator and denominator:

`color(red)((color(green)(cancel(color(red)((n + 3))))(n + 4)) xx color(purple)((color(blue)(cancel(color(purple)(2)))color(blue)(cancel(color(purple)(n))))))/(color(blue)((color(purple)(cancel(color(blue)(16)))8color(purple)(cancel(color(blue)(n^2)))n)) xx color(red)(cancel(color(green)((n + 3))))) =>`

`(n + 4)/(8n)`