Completely simplify the following expression and indicate the restrictions on the variable x

Question

Expression:

https://photos.app.goo.gl/GxS1oif7SYFyAEJb8

I don't understand. Doesn't the expression equal to 1? So that means that I can't simplify it and find the restrictions on x, right?? My brain hurts

Answer 1

You are correct that the expression would simplify to 1. When factored, all expressions factor to their binomial terms, and all terms cancel, so the expression DOES equal 1.

With respect to the restrictions on x, they are asking about what values of x can the expression NOT equal because it would produce a 0 in the denominator. In this case, this is for the first fraction (denominator), second fraction (denominator), and third fraction (the numerator, because the fraction will be flipped).

We need to set all of these terms equal to zero and solve:

1.) 2x²+x-6 = 0 --> x = 3/2 and x = -2

2.) x+1 = 0 --> x = -1

3.) 2x-3=0 --> x = 3/2

Therefore, the restricted values of x are x = -2, -1, and 3/2

If you were to graph this expression on a graphing calculator or a website such as Desmos, there will be holes in the graph at x = -2, -1, and a vertical asymptote at x = 3/2.