Question

Which of the following is equal to the rational expression when x does not equal -2 or-1

Answer 1

Given the expression:

`(x^2-4)/((x+2)(x+1))`

notice that on the numerator we have a square conjugate, then, we can factorize it like this:

`x^2-4=(x+2)(x-2)`

doing this on the original expression, we havE:

`(x^2-4)/((x+2)(x+1))=((x+2)(x-2))/((x+2)(x+1))=(x-2)/(x+1)`

therefore, the expression (x-2)/(x+1) is equivalent to the given expression