Answer: [tex]\frac{-2p^2+10p-8}{p^2-4}[/tex]
This can be written as (-2p^2+10p-8)/(p^2-4) on a keyboard.
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Work Shown:
[tex]\frac{2p}{p^2-4} + \frac{4-2p}{p+2}\\\\\\\frac{2p}{(p+2)(p-2)} + \frac{4-2p}{p+2}\\\\\\\frac{2p}{(p+2)(p-2)} + \frac{(4-2p)(p-2)}{(p+2)(p-2)}\\\\\\\frac{2p+(4-2p)(p-2)}{(p+2)(p-2)}\\\\\\\frac{2p-2p^2+8p-8}{p^2-4}\\\\\\\frac{-2p^2+10p-8}{p^2-4}\\\\\\[/tex]
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Explanations:
- In step 2, I factored p^2-4 using the difference of squares rule.
- In step 3, I multiplied top and bottom by (p-2) so that the second fraction has a denominator of (p+2)(p-2). We can only add fractions that have the same denominator.
- In step 5, I used the FOIL rule to expand (4-2p)(p-2) into -2p^2+10p-8. You can use the distribution rule or the box method as alternatives.
