Question

What is the LCD between `x/(x^2 - 81 )` and `(3x)/(x^2+18x +81)`?

Answer 1

Since
`x/(x^2-81) = (x)/(color(red)((x+9))color(green)((x-9)))`
and
`(3x)/(x^2+18x+81) = (3x)/(color(red)((x+9))color(blue)((x+9)))`

The Least Common Denominator of the two given expressions is
`(x+9)^2(9-x)`

Please note that that the LCD is the product of the common and non-common factors of the given expressions.