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Consider the expressions \(\frac{4x^3+2x^2+6x+7}{2x+1}\) and \(2x^2+3+\frac4{2x+1}\)

a) Show that these expressions are equal when x=10

b) Explain why these expressions are not equal when x=-1/2

c) Show that these expressions are equal for all x other than -1/2

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

 

IMPORTANT:
Your first instinct on Part (c) may be to manipulate an equation until both sides are equal. However, this can confuse your reader: you would be writing equations that you don't know are true! Try to write your solution so that every equation you write is true​

 Jan 27, 2019
 #1
avatar+102434 
+1

Here's part (c)

 

2x^2  + 3   +   [ 4 ] / (2x + 1)     can be simplified as

 

[ (2x^2 + 3)(2x + 1)  + 4 ] / [ 2x + 1] =

 

  [ 4x^3 + 2x^2 + 6x + 7 ]  / [ 2x + 1] 

 

Which is equal to the first function

 

With this in mind....(a)  must be true

 

 

 

 

cool cool cool

 Jan 27, 2019
 #2
avatar+57 
+1

Part b)

When x=-1/2. the denominator of the first expression becomes undefined. When x=-1/2, the second expression's third term becomes undefined too. Therefore, they are not equal because the first expression is entirely undefined while the second expression has only one term undefined.

 Jan 27, 2019

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