Find the partial fraction decomposition.

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

(2x^2-x+4)/ x^3+4x

May 15th, 2015

Factor the denominator and then the fraction may be written in the form:

(2x2 – x + 4)/(x3 + 4x) = (2x2 – x + 4)/ [x(x2 + 4)] = A/x + (Bx + C)/(x2 + 4)

Multiply both sides by x3 + 4x. Then for all x we have 2x2 – x + 4 = A(x2 + 4) + (Bx + C)x .

Substitute x = 0 into the previous identity. Then 4 = 4A and A = 1.

Write the coefficients at x and at x2:  –1 = C,  2 = A + B,  and B = 2 – A = 1.

Answer: (2x2 – x + 4)/(x3 + 4x) =1/x + (x – 1)/(x2 + 4).


May 15th, 2015

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
May 15th, 2015
...
May 15th, 2015
Sep 26th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer