Question

What is the LCD of the following rational expressions?

x/x+1 , 7x/x-1

please help I'm so confused!?

Answer 1

`(x)/(x+1) \ , \ (7x)/(x-1)`


`(x (x -1))/((x+1)(x -1)) \ , \ (7x(x+1))/((x-1)(x+ 1))`

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


`(x (x -1))/(x^2 - 1)} \ , \ \frac{7x(x+1)} {x^2 - 1}`

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

Answer 2

`(x)/(x + 1)`,
`(7x)/(x - 1)`

To find the least common denominator, multiply
`(x)/(x + 1)` by (x - 1) and multiply
`(7x)/(x - 1)` by (x + 1).

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

x² - 1 is the LCD.