Question

Simplify each expression and state any non-permissible values. (4 marks - show your work)

x^2-2x divided by x+1 multiplied by x^2-1 divided by x^2+x-6 is the expression

Answer 1

x(x-2) /(x+1) * (x+1)(x-1)/[(x+3)(x-2)]

= x (x-1)/(x+3)

Answer 2

I read that as:

(x^2 - 2x)/(x+1) * (x^2 - 1)/(x^2 + x - 6)

=x(x-2)/(x+1)*(x-1)(x+1)/( (x+3)(x-2)
= x(x-1)/(x+3) or (x^2 - x)/(x+3) , x ≠ -1,2

Answer 3

I think it just blows up if x = -3

Answer 4

The inclusive vs exclusive restrictions in rational expressions always leads to debate.

I restricted x = -1 and x = -2 since subbing in these values in the original yields 0/0 but subbing those values in my answer (and yours) yields a real number
Since I was using the equal sign, the original is not equal to the final expression for x = -1, 2

but I did not state that x ≠ 3 since by default
the expression blows up in both the original and the final answer.
Some texts will state as restrictions all that cause a zero at the bottom, while others use the limitations I stated.