Question

What is the LCD of the following rational expressions?

Answer 1

$\dfrac{x}{x+1} \ , \ \dfrac{7x}{x-1}$

$\dfrac{x (x -1)}{(x+1)(x -1)} \ , \ \dfrac{7x(x+1)}{(x-1)(x+ 1)}$

We know that (a + b)(a - b) = a² - b²:

$\dfrac{x (x -1)}{x^2 - 1}} \ , \ \dfrac{7x(x+1)} {x^2 - 1}$

Answer: LCD = ( x + 1) (x - 1)

Answer 2

$\frac{x}{x + 1}$, $\frac{7x}{x - 1}$

To find the least common denominator, multiply $\frac{x}{x + 1}$ by (x - 1) and multiply $\frac{7x}{x - 1}$ by (x + 1).

(x + 1)(x - 1) = x² - x + x - 1 ⇒ x² - 1

x² - 1 is the LCD.