Question

How do you multiply and simplify `\frac { 3x } { x ^ { 2} - 36} \cdot \frac { x + 6} { 9x }`?

Answer 1

Multiply the numerators and denominators then simplify.

`3x(x + 6) = 3x^2 +18x`

`9x(x^2 - 36) = 9x^3 - 324x`

`(3x^2 +18x)/(9x^3 - 324x) = (3x(x + 6))/(9x(x^2 - 36))`

`(x + 6)/(3(x^2 - 36)) = (x+6)/(3(x+6)(x-6)) =1/(3x-18)`