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

1 Answer
Aug 31, 2017

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