Answer:
[tex]\frac{x-2}{x^2-x-2}[/tex]
Step-by-step explanation:
A removable discontinuity is when there is a hole in your graph. This is usually because one X value has been canceled out. Most of the time, it takes factoring to figure out if there is a removable discontinuity when looking at an equation.
First, look at the numerator [tex]x-2[/tex] . This can't be factored any further. However, [tex]x^2-x-2[/tex] can be factored since it is a trinomial (has three terms) .
For the purposes of this example, you may want to think about it as
[tex]1x^2 -1x-2[/tex]
To factor, multiply the the outside coefficients
1 x -2 = -2
Now take the middle coefficient (-1) and ask yourself what two numbers multiply to make -2, but still add to be -1.
-2 x 1 = -2
-2 + 1 = -1
So in factored form, the equation is
[tex]\frac{x-2}{(x-2)(x+1)}[/tex]
Since you have x-2 on both top and bottom, that can be canceled out. x - 2 would be your removable discontinuity in this situation.
