Question

How do you multiply and simplify `\frac { 14x } { x + 9} \cdot \frac { 4x + 36} { 7x }`?

Answer 1

See a solution process below:

Explanation:

First, factor the numerator on the left as:

`(14x)/(x + 9) * (4(x + 9))/(7x)`

Next, cancel common terms across the numerations and denominators:

`(color(red)(cancel(color(black)(14)))2color(blue)(cancel(color(black)(x))))/color(orange)(cancel(color(black)(x + 9))) * (4color(orange)(cancel(color(black)((x + 9)))))/(color(red)(cancel(color(black)(7)))color(blue)(cancel(color(black)(x)))) => 8`

Because we cannot divide by `0`, going back to the original equation this is true for every value except for:

`x + 9 = 0` and `7x = 0`

Or `x = -9` and `x = 0`