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Consider the equation

 

(4x^3 + 2x^ 2+ 10x + 9)/(2x + 1) = 2x^2 + 5 + 4/(2x + 1)

a) Show that this equation is true when x = 10

b) Explain why this equation is not true when x = -1/2.

c) Show that this equation is true for all x  other than x = -1/2.

In parts (a) and (c), begin by explaining what your strategy for solving will be.

Your first instinct on Part (c) may be to manipulate the equation until both sides are equal. However, this can confuse your reader: you would be writing equations that you don't know are true! Reread your solution when you're finished. Make sure that your solution points out all of the equations that you don't know are true yet. Or try to write your solution so that every equation you write is true.

 Oct 10, 2020
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A    put in x=10   to show the same value is calculated on each side of the equation

B   x cannot be -1/2     the denominator would be zero....not allowed

C   Put Right side over common denominator (2x+1)

 

     [   2x^2 (2x+1)  + 5 (2x+1) + 4 ]   / (2x+1)

        [ 4x^3 + 2x^2  + 10x + 5 + 4  ] / (2x+1)      This exactly the same as the expression on the LEFT

                           so any 'x' value (except -1/2) will make this equation true

 Oct 10, 2020

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