Question

How do you multiply and simplify `\frac { 6} { 4n + 10} \cdot \frac { 8n + 20} { 6}`?

Answer 1

See the entire solution process below:

Explanation:

First, cancel the common term in the numerator and denominator of each fraction:

`6/(4n + 10) * (8n + 20)/6 -> color(red)(cancel(color(black)(6)))/(4n + 10) * (8n + 20)/color(red)(cancel(color(black)(6))) ->`

`1/(4n + 10) * (8n + 20)/1 -> (8n + 20)/(4n + 10)`

Next, factor a `color(red)(4)` out of the numerator and a `color(blue)(2)` out of the denominator:

`((color(red)(4) xx 2n) + (color(red)(4) xx 5))/((color(blue)(2) xx 2n) + (color(blue)(2) xx 5)) = (color(red)(4)(2n + 5))/(color(blue)(2)(2n + 5))`

Again, cancel out the common terms in the numerator and denominator:

`(4color(red)cancel(color(black)((2n + 5))))/(2color(red)cancel(color(black)((2n + 5)))) -> 4/2 -> 2`

However, we need to remember `4n + 10 != 0` or `n != 2.5`