SOLUTION: Find the partical fraction decomposition for the following rational expression: 4x^2-5x-15/x(x+1)(x-5)
Algebra.Com
Question 679682: Find the partical fraction decomposition for the following rational expression: 4x^2-5x-15/x(x+1)(x-5)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the partial fraction decomposition for the following rational expression: 4x^2-5x-15/x(x+1)(x-5)
-----
4x^2-5x-15/[x(x+1)(x-5)] = A/x + B/(x+1) + C/(x-5)
----------
4x^2-5x-15 = [A(x+1)(x-5)] + [Bx(x-5)] + [Cx(x+1)]
-------
4x^2-5x-15 = Ax^2-4Ax-5A + Bx^2 - 5Bx + Cx^2 + Cx
-----
4x^2-5x-15 = (A + B + C)x^2 + (-4A-5B+C)x + (-5A)
-------
Equation:
A + B + C = 4
-4A-5B+C = -5
-5A = -15
--------
A = 3
------
Substitute 3 for A to get:
B + C = 1
-5B+C = 7
---------
Subtract and solve for "B":
6B = -6
B = -1
------
Solve for "C":
C = 2
---------
4x^2-5x-15/[x(x+1)(x-5)] = 3/x - 1/(x+1) + 2/(x-5)
=====================
Cheers,
Stan H.
=====================
RELATED QUESTIONS
partial fraction decomposition; use the partical fraction decomposition to "decompose"... (answered by venugopalramana)
Write the partial fraction decomposition of each rational expression.
x/x^2-5x+6
(answered by robertb)
Hi, i'm really stuck on this problem for partial fractions and would really appreciate... (answered by ankor@dixie-net.com)
Find the partial fraction decomposition for each rational expression.... (answered by jsmallt9)
Write the partial fraction decomposition of the rational expression:... (answered by Edwin McCravy,DrBeeee)
Write the partial fraction decomposition of the rational expression:... (answered by DrBeeee)
find the partial fraction decomposition :... (answered by Edwin McCravy)
Write the partial fraction decomposition of the following rational expression.
{{{... (answered by greenestamps)
Write the partial fraction decomposition of the rational expression... (answered by Fombitz)