How do you express #x^2 /(x^2 +x+2)# in partial fractions?
1 Answer
Answer
Answer:
Explanation
Explanation:
Answer:
See below.
Explanation:
Question:
How do you express

A) "Partial fractions can only be done if the degree of the numerator is strictly less than the degree of the denominator. That is important to remember."
From: http://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx 
B) A well written discussion of partial fractions can be found here: http://www.purplemath.com/modules/partfrac.htm
Given:
The discriminant for the denominator:
As in reference A), above, a case such as ours, the procedure is to do long division to obtain a fraction that might be written in partial fraction form.
So,
Concentrate on the fraction, then we can put it back together. Since the denominator can not be factored with real numbers, we leave it alone and write:
Then, solve for A and B.
The denominators are the same, so the numerators must be equal.
The only way that can happen is if A = 1, and B = 2.
Putting it back together:
This expression looks familiar, but it is all we can do!
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