Answer:
Excluded values -2,0,2 These are non removable since we cannot cancel them in the numerator
(x+1)
---------
x(x+2)
Step-by-step explanation:
-2 x-1
----------- + ---------
x^2 -4 x^2 -2x
First factor the denominators
-2 x-1
----------- + ---------
x^2 -4 x^2 -2x
x^2 -4 is the difference of squares
x^2 -4 = (x-2) (x+2)
x^2 -2x has an x in common
x(x-2)
-2 x-1
----------- + ---------
(x-2)(x+2) x(x -2)
The values that are excluded are the values that make the denominators zero
(x-2) (x+2) = 0 x=2 x=-2
x(x-2) =0 x=0 x=2
Excluded values -2,0,2 These are non removable since we cannot cancel them in the numerator
We need to get a common denominator of (x-2)(x+2)x
Multiply the first term by x/x and the second term by (x+2)/(x+2)
-2 x (x-1) (x+2)
----------- + ----------------
x(x-2)(x+2) x(x -2)(x+2)
Distribute
(x+2)(x-1) = x^2 -x+2x-2 = x^2+x-2
-2 x x^2+x-2
----------- + ----------------
x(x-2)(x+2) x(x -2)(x+2)
Combine like terms, since the denominators are the same
-2 x + x^2+x-2
---------------------------
x(x-2)(x+2)
x^2-x-2
---------------------------
x(x-2)(x+2)
Factor the numerator
x^2-x-2 = (x-2) (x+1)
(x-2) (x+1)
---------------------------
x(x-2)(x+2)
Cancel like terms
(x+1)
---------------------------
x(x+2)
The excluded values are found at the beginning, not now. We canceled some of them in our simplified expression. They are still excluded values
