Simplify the following rational expression. List all of the excluded values, and classify each as a removable discontinuity, or a nonremovable discontinuity. -2/x^2-4+x-1/x^2-2x

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What have they told you? What does it mean? What more do you know or can you figure out? What connections can you make? Do you have a list of things you know, ideas to try & a plan for doing it?

Solve by showing steps towards completing the problem, including writing/using equations. Revise your plan if it doesn’t work the first time. Check your work. No guess and check.

Look back at your work and answer – does it make sense, answer all of the questions, and is reasonable (accurate)? When it is - Organize and report your work and final answer. Look back at your work and answer – does it make sense, answer all of the questions, and is reasonable (accurate)? When it is - Organize and report your work and final 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

mariah is studying the life cycle of the monarch butterfly. she must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. she plans to make her choice randomly using a custom spinner divided into four sections. first, however, she spins the spinner 50 times to see the frequencies it generates.

stage times landed on

egg 10

caterpillar 12

chrysalis 15

adult 13

step-by-step explanation: