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AlpenGlow
[tex] (p^{2} + p - 6) - (x) = p - 9 [/tex] is what is asked.

So all you need to do is a value that will result to p - 9.

x = [tex] (p^{2} + p - 6) - p + 9 [/tex]  To isolate x we just transpose the values from the other side of the equation and do the opposite operation. 

Combine like terms and just copy the terms that do not have similar expressions:

p will cancel out because p - p = 0
-6 and + 9  will come together because they are like terms: -6 + 9 = 3 
[tex] p^{2} [/tex] does not have a pair so it will remain as is. you will be left with:

[tex] p^{2} + 3[/tex]

Let us check:

   [tex]p^{2} + p - 6[/tex]
-  [tex]p^{2} + 0 + 3 [/tex]  
----------------------------
   [tex]0 + p - 9[/tex]    or [tex]p -9[/tex]               

Answer:

We have to subtract [tex]p^2+3[/tex] from the given expression to obtain a difference of [tex]p-9[/tex]

Step-by-step explanation:

We are given the following information in the question:

We are given an expression:

[tex]p^2 + p -6[/tex]

We subtract [tex]p^2 - 4p[/tex] from the given expression.

[tex]p^2 + p -6 - (p^2 - 4p)\\= (p^2 - p^2) + (p + 4p)-6\\=5p - 6[/tex]

Now, we want to obtain the difference as [tex]p-9[/tex]

Let x be the expression we subtract from the given expression, then we can write:

[tex]p^2 + p -6 - x = p-9\\p^2 +p -6-(p-9) = x\\x = p^2+(p-p)+(-6+9)\\x = p^2+3[/tex]

Thus, we have to subtract [tex]p^2+3[/tex] from the given expression to obtain a difference of [tex]p-9[/tex]

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