SOLUTION: Find the partial fraction decomposition of the rational expression below. (-x-37)/(x^2-3x-28) a.-(4/x-7)-(3/x+4) b.(3/x-7)+(3/x+4) c.-(3/x-7)+(3/x+4) d.(4/x-7)+(3/x+4) e.

Question 471722: Find the partial fraction decomposition of the rational expression below.
(-x-37)/(x^2-3x-28)
a.-(4/x-7)-(3/x+4)
b.(3/x-7)+(3/x+4)
c.-(3/x-7)+(3/x+4)
d.(4/x-7)+(3/x+4)
e.-(4/x-7)+(3/x+4)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the partial fraction decomposition of the rational expression below.
(-x-37)/(x^2-3x-28)
----
[-(x+37)]/[(x-7)(x+4)]
----
= A/(x-7) + B/(x+4)
----
= [A(x+4) + B(x-7)]/[x^2-3x-28]
----
Equate the numerators:
(A+B)x + (4A-7B) = -x-37
---
Then:
A + B = -1
4A-7B = -37
----
Modify:
4A + 4B = -4
4A - 7B = -37
----
11B = 33
B = 3
---
Since A+B = -1
A = -4
----
Solution:
-4/(x-7) + 3/(x+4)
------------------------
Cheers,
Stan H.
========================
a.-(4/x-7)-(3/x+4)
b.(3/x-7)+(3/x+4)
c.-(3/x-7)+(3/x+4)
d.(4/x-7)+(3/x+4)
e.-(4/x-7)+(3/x+4)

RELATED QUESTIONS
Perform partial fraction decomposition for the expression 8+x+6x^2-12x^3/... (answered by MathLover1,MathTherapy,greenestamps)

Find the partial fractional decomposition of the rational expression. {{{... (answered by josgarithmetic)

Write the partial fraction decomposition of the rational expression. x-6... (answered by Fombitz)

Write the partial fraction decomposition of the rational expression:... (answered by DrBeeee)

Write the partial fraction decomposition of the rational expression... (answered by Fombitz)

Solve the partial fraction decomposition of the rational expression: (3x^2+49) /... (answered by stanbon)

Write the partial decomposition of the rational expression: (-x^2+2x+4)/(x(x+2)^2) =... (answered by stanbon,Edwin McCravy)

Write the partial fraction decomposition of each rational expression. x/x^2-5x+6 (answered by robertb)