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#