Question

How do you simplify and find the restrictions for `( (x^2 -x-12)/( x^2 -2x-15) ) / ( (x^2 + 8x+12)/( x^2 -5x-14))`?

Answer 1

The expression simplifies to `((x - 4)(x + 7))/((x - 5)(x + 6))` with restrictions being `x!= 5, -3, -6, 7 and -2`.

Explanation:

`=(((x - 4)(x + 3))/((x - 5)(x + 3)))/(((x + 6)(x + 2))/((x - 7)(x + 2))`

`=((x - 4)/(x - 5))/((x + 6)/(x + 7))`

`=((x -4)(x + 7))/((x - 5)(x + 6))`

Restrictions occur when the denominator of the original expression equal `0`. We can determine restrictions by setting the denominator to `0` and solving.

`(x - 5)(x + 3) = 0`

`x = 5 and -3`

AND

`(x + 6)(x + 2) = 0`

`x = -6 and -2`

AND

`(x - 7)(x + 2) = 0`

`x = 7 and -2`

Hopefully this helps!