Discuss: Recognizing Partial Fraction Decompositions For each expression, determine whether it is already a partial fraction decomposition or whether it can be decomposed further. a) xx2+1+1x+1 b) x(x+1)2 c) 1x+1+2(x+1)2

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Discuss: Recognizing Partial Fraction Decompositions  For each expression, determine whether it is already a partial fraction decomposition or whether it can be decomposed further.  a) xx2+1+1x+1  b) x(x+1)2  c) 1x+1+2(x+1)2

StrycharzT · Accepted Answer

Step 1  We have to see if the given fractions are partially fraction decomposition or if they can be decomposed further.  For partially fraction, we have to factor the denominator and write it separately in the fraction  Step 2 Part a  We have the fraction  xx2+1+1x+1+1x+1  Here we can see that the fractions are already factored and written separately.  Hence this fraction is already partially decomposed.  Step 3 Part b  Here we have the fraction  x(x+1)2  If we see the denominator, it can further be factored as  x(x=1)2=A(x+1)+B(x+1)2  Therefore, the given fraction was not partially decomposed.   Step 4 Part c  Here we have the fraction  1x+1+2(x+1)2  The fraction given here is already partially decomposed as the denominator given here is already partially decomposed.   Note- since you have posted a question with multiple subparts, we will solve only first three subparts for you. To get the remaining done please resubmit the complete question and mention the subparts to be solved.

Discuss: Recognizing Partial Fraction Decompositions For each expression, de

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