What is the LCD between $\frac{x}{x^{2} - 81}$ $x/(x^2 - 81 )$ and $\frac{3 x}{x^{2} + 18 x + 81}$ $(3x)/(x^2+18x +81)$ ?

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What is the LCD between $\frac{x}{x^{2} - 81}$ $x/(x^2 - 81 )$ and $\frac{3 x}{x^{2} + 18 x + 81}$ $(3x)/(x^2+18x +81)$ ?

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Answer 1 · 2015-05-27T11:24:38

Since
$\frac{x}{x^{2} - 81} = \frac{x}{(x + 9) (x - 9)}$ $x/(x^2-81) = (x)/(color(red)((x+9))color(green)((x-9)))$
and
$\frac{3 x}{x^{2} + 18 x + 81} = \frac{3 x}{(x + 9) (x + 9)}$ $(3x)/(x^2+18x+81) = (3x)/(color(red)((x+9))color(blue)((x+9)))$

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

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

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What is the LCD between $\frac{x}{x^{2} - 81}$ $x/(x^2 - 81 )$ and $\frac{3 x}{x^{2} + 18 x + 81}$ $(3x)/(x^2+18x +81)$ ?

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What is the LCD between xx2−81x/(x^2 - 81 ) and 3xx2+18x+81(3x)/(x^2+18x +81)?

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What is the LCD between $\frac{x}{x^{2} - 81}$ $x/(x^2 - 81 )$ and $\frac{3 x}{x^{2} + 18 x + 81}$ $(3x)/(x^2+18x +81)$ ?